THE DEVELOPMENT OF A MINIATURE FLEXIBLE FLAPPING
WING MECHANISM FOR USE IN A ROBOTIC AIR VEHICLE
A Thesis
Presented to
The Academic Faculty
by
Gautam Jadhav
In Partial Fulfillment
Of the Requirements for the Degree
Master of Science in the
School of Mechanical Engineering
Georgia Institute of Technology
May 2007
i
THE DEVELOPMENT OF A MINIATURE FLEXIBLE FLAPPING
WING MECHANISM FOR USE IN A ROBOTIC AIR VEHICLE
Approved by:
Dr. Kevin C. Massey, Advisor
Georgia Tech Research Institute
Georgia Institute of Technology
Dr. Wayne J. Book, Advisor
School of Mechanical Engineering
Georgia Institute of Technology
Dr. David W. Rosen
School of Mechanical Engineering
Georgia Institute of Technology
Date Approved: March 8, 2007
ii
ACKNOWLEDGEMENTS
I wish to thank my thesis advisor, Dr. Kevin Massey for his guidance in this
research. I am grateful for the lessons learned under him and the time he took to work
with me.
I would like to thank my academic advisor, Dr. Wayne Book for his guidance in
my academic endeavors.
I would like to thank Dr. David Rosen for being on my thesis reading committee
and taking the time to read this thesis.
Lastly, I would also like to thank my mother and father for their support, without
which I would not be here.
iii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
iii
LIST OF TABLES
viii
LIST OF FIGURES
ix
LIST OF SYMBOLS AND ABBREVIATIONS
xiii
SUMMARY
xiv
CHAPTER 1: INTRODUCTION
1
CHAPTER 2: LITERATURE SURVEY
3
2.1
Lift Generation in Flapping Wing Flight
3
2.2
Thrust Generation in Flapping Wing Flight
5
2.3
Flexible Wings versus Rigid Wings
6
2.4
Current UAVs and Flapping Wing Mechanisms
7
2.5
Wing Geometries of Natural Flappers
12
2.6
Missing Links in Current Research
14
CHAPTER 3: MECHANICAL DESIGN REQUIREMENTS
15
3.1
Objective
15
3.2
Weight Requirements
15
3.3
Wingspan and Planform Requirements
15
3.4
Flapping Frequency and Speed Requirements
16
3.5
Summary of Requirements
17
CHAPTER 4: DESIGN PROCESS
18
4.1
18
Mechanism
iv
4.2
Materials and Dimensions Used
29
4.3
Mechanism Electronics
30
4.4
Weight Reduction Efforts
31
4.5
Wings
33
4.5.1
Wing Fabrication Process
34
4.5.2
Wing Flexibility
36
CHAPTER 5: EXPERIMENTAL APPARATUS
43
5.1
Force Balance
43
5.2
Springs
47
5.3
Wind Tunnel Modification
48
CHAPTER 6: TEST EQUIPMENT CALIBRATION
50
6.1
50
6.2
6.3
6.4
Calibration of Potentiometers
6.1.1
Measuring Spring Deflection: Position Transducers
50
6.1.2
Wiring
51
6.1.3
Distance Calibration and LabView
51
Calibration of Force Balance
53
6.2.1
Calibration of ±X Direction (Thrust)
53
6.2.2
Calibration of ±Y Direction (Lift)
54
Calibration of Motor and Encoder
56
6.3.1
Wiring of Motor
56
6.3.2
Wiring of the Optical Encoder
56
6.3.3
Encoder Calibration and LabView
57
Data Acquisition
58
v
6.5
Angle of Attack Calibration
58
CHAPTER 7: TESTING
60
7.1
Testing Approach: Test Matrix
60
7.2
Encoder Position, Wing Tip and Root Position Correlation
62
7.3
Filtering of Force Balance Inertial Effects
64
7.4
Aerodynamic Forces Generated Without Flapping
66
CHAPTER 8: ANALYSIS OF RESULTS
69
8.1
Wing 1 Phase Lag
69
8.2
Wing 2 Phase Lag
73
8.3
Wing Pitching Motions
76
8.4
Analysis of 1st Generation Wing
78
8.5
8.6
8.4.1
Results: Lift and Thrust Force vs. Time
78
8.4.2
Results: Lift and Thrust Force vs. Wing Position (Phase)
80
8.4.3
Lift and Thrust Data to High Speed Video Correlation
82
8.4.4
Wing 1 Velocity Analysis
89
Analysis of 2nd Generation Wings
92
8.5.1
Lift and Thrust Data to High Speed Video Correlation
8.5.2
Wing 2 Velocity Analysis
92
102
Summary of Wing 1 and Wing 2 Performance
104
CHAPTER 9: UNCERTAINTY ANALYSIS
108
9.1
Force Balance Uncertainty
108
9.2
Lift and Thrust Uncertainty
109
CHAPTER 10: CONCLUDING REMARKS
vi
114
10.1
Summary
114
10.2
Contributions to Research Area
117
10.3
Future Work
118
APPENDIX A: CALIBRATION DATA
120
APPENDIX B: PLOTS
122
REFERENCES
128
vii
LIST OF TABLES
Table 3.1: Target Design Requirements
17
Table 4.1: Table of Mechanism Weights Before and After Weight Reduction Efforts
33
Table 4.2: Weights Applied to Structural Points of Wing 1
38
Table 4.3: Distributed Loading on Flexible Wing
40
Table 4.4 Weights Applied to Structural Points of Wing 2
40
Table 4.5: Stiffness Increases from Wing 1 to Wing 2 per Point
41
Table 5.1: Summary of Springs Used for Centering Mechanism in Test Apparatus
47
Table 7.1: Test Matrix for Wing 1
60
Table 7.2: Test Matrix for Wing 2
61
Table 8.1: Summary of Experimental Results
104
Table 9.1: Error Analysis for Force Balance
108
Table A.1: Spring Constant Calibration Data
120
Table A2: Averaged Values of Spring Calibration Data
121
viii
LIST OF FIGURES
Figure 2.1: Unit Force vs. Time for Up and Down Strokes [4]
4
Figure 2.2: Average Lift vs. Frequency [3]
4
Figure 2.3: Lift and Thrust Generation vs. Phase [5]
5
Figure 2.4: Average Thrust vs. Frequency [3]
6
Figure 2.5: Flexible Wing UAV Developed at the University of Florida [9]
9
Figure 2.6: Mechanism Capable of Biaxial Rotation [14]
10
Figure 2.7: Microbat Transmission System and Fabricated UAV [15]
11
Figure 2.8: Drive Mechanism in Toronto Ornithopter [16]
11
Figure 2.9: High Speed Video of Bat Wing [20]
13
Figure 3.1: Planform of a Bat’s Wing Showing Structural Members [22]
16
Figure 3.2: Flight Speed of Flyers vs. Mass [6]
17
Figure 4.1: Isometric View of Entire Flapping Mechanism (CAD Model)
18
Figure 4.2: Top View of Flapping Mechanism (CAD Model)
19
Figure 4.3: Left Side View of Flapping Mechanism (CAD Model)
20
Figure 4.4: Speed vs. Torque Curve for 2232 Micromo Motor [24]
23
Figure 4.5: Close-Up View (Top) of Drive Mechanism (CAD Model)
24
Figure 4.6: Close-Up of Flywheel and Crankshaft Connecting Pins (CAD Model)
25
Figure 4.7: Close-Up of Swivel Joints and Pitching Assembly (CAD Model)
27
Figure 4.8: Isometric View of Flapping Device
28
Figure 4.9: Top View of Flapping Device (Without Motor and Coupling)
28
Figure 4.10: Front View of Flapping Device
29
ix
Figure 4.11: Close-Up View of Swivel Joints After Weight Reduction Efforts
29
Figure 4.12: Encoder Hub Disk and Module Used
31
Figure 4.13: Isometric View of Mechanism After Weight Reduction Efforts
32
Figure 4.14: Top View of Mechanism After Weight Reduction Efforts
32
Figure 4.15: View of Wing Mold – One Half (CAD Model)
36
Figure 4.16: 7 Structural Points of Flexible Wing 1
37
Figure 4.17: Wing 1 Stiffness Curves
39
Figure 4.18: Wing 2 Stiffness Curves
41
Figure 5.1: Test Superstructure and Flapping Mechanism (CAD Model)
43
Figure 5.2: Close-Up of Linear Bearing Housing Assembly (CAD Model)
45
Figure 5.3: Close-Up of Mechanism on Center Shaft (CAD Model)
46
Figure 5.4: Actual View of Mechanism in Test Assembly
47
Figure 5.5: Actual View of Wind Tunnel After Modifications
49
Figure 6.1: View of Force Measurement for Drag and Thrust
54
Figure 6.2 : View of Measuring Spring Constant of Bottom Spring
55
Figure 6.3: Angle of Attack Calibration Tool
59
Figure 7.1: Encoder Position, Wing Root & Tip Displacements vs. Time
64
Figure 7.2: Setup for Spring Dynamics Correction
65
Figure 7.3: Lift & Drag Force vs. Time @ 5 m/s Without Flapping
67
Figure 7.4: Lift vs. Angle of Attack @ 5 m/s Without Flapping
68
Figure 8.1: High Speed Video Still Image of Wing 1 Beginning Upstroke
69
Figure 8.2: High Speed Video Still Image of Wing 1 on Downstroke
70
Figure 8.3: Wing 1 Root & Tip Displacement with Curve Fits
71
x
Figure 8.4: High Speed Video Still Image of Wing 2 Beginning Upstroke
74
Figure 8.5: High Speed Video Still Image of Wing 2 Beginning Downstroke
74
Figure 8.6: Wing 2 Root & Tip Displacement with Curve Fits
75
Figure 8.7: Wing 1 Pitching Motions Produced During Flapping
77
Figure 8.8: Lift & Thrust vs. Time @ 0 m/s, 3 Hz, & 0° AoA
79
Figure 8.9: Lift & Thrust vs. Phase @ 0 m/s, 3 Hz, & 0° AoA
80
Figure 8.10: Wing 1 Position, Force & Phase Correlation @ 0 m/s, 3 Hz, & 0° AoA
84
Figure 8.11: Wing 1 Position, Force & Phase Correlation @ 5 m/s, 3 Hz, & 7.5° AoA 86
Figure 8.12: Wing 1 Position, Force & Phase Correlation @ 5 m/s, 4 Hz, & 7.5° AoA 87
Figure 8.13: Wing 1 Position, Force & Phase Correlation @ 5 m/s, 4 Hz, & 7.5° AoA 88
Figure 8.14: High Speed Video Showing Stall @ 5 m/s, 4 Hz, 15° AoA
89
Figure 8.15: Wing 2 Position, Force & Phase Correlation @ 0 m/s, 3 Hz, & 0° AoA
93
Figure 8.16: Wing 2 Position, Force & Phase Correlation @ 5 m/s, 3 Hz, & 7.5° AoA 95
Figure 8.17: Relative AoAs for Wing1 and Wing 2, 4 inches Outboard from Root
96
Figure 8.18: Relative AoAs for Wing 1 and Wing 2, at the ¾ Span Point
98
Figure 8.19: Wing 2 Position, Force & Phase Correlation @ 5 m/s, 4 Hz, & 7.5° AoA 99
Figure 8.20: Aerodynamic Force Vectors vs. Wing Position in Flapping Cycle
100
Figure 8.21: Wing 2 Position, Force & Phase Correlation @ 5 m/s, 4 Hz, & 15° AoA 101
Figure 8.22: Lift & Thrust vs. Phase @ 0 m/s, 3 Hz, & 0° AoA
106
Figure 8.23: Lift & Thrust vs. Phase @ 5 m/s, 3 Hz, & 7.5° AoA
106
Figure 8.24: Lift & Thrust vs. Phase @ 5 m/s, 4 Hz, & 7.5° AoA
107
Figure 8.25: Lift & Thrust vs. Phase @ 5 m/s, 4 Hz, & 15° AoA
107
Figure 9.1: Uncertainty Curve for 5 m/s, 4 Hz, 7.5° AoA with Wing 2
110
xi
Figure 9.2: Repeatability 5 m/s, 4 Hz, 7.5° AoA with Wing 2
111
Figure 9.3: Uncertainty Curve for 0m/s, 3 Hz, 0° AoA with Wing 1
112
Figure A.1: Spring Constant Data for Force Balance Calibration
120
Figure B.1: Wing 1 Root, Tip & Encoder Position vs. Time @ 0 m/s, 2 Hz, 7.5° AoA 122
Figure B.2: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 2 Hz, 7.5° AoA 122
Figure B.3: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 3 Hz, 0° AoA
123
Figure B.4: Wing 1 Root, Tip & Encoder Position vs. Time @ 0 m/s, 3 Hz, 7.5° AoA 123
Figure B.5: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 3 Hz, 7.5° AoA 124
Figure B.6: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 4 Hz, 0° AoA
124
Figure B.7: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 4 Hz, 7.5° AoA 125
Figure B.8: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 4 Hz, 15° AoA 125
Figure B.9: Lift & Thrust Force vs. Phase at 0 & 5 m/s, 2 Hz, & 7.5° AoA
126
Figure B.10: Lift & Thrust vs. Phase at 0 m/s, 3 Hz, & 0° & 7.5° AoA
126
Figure B.11: Lift & Thrust vs. Phase at 5 m/s, 3 Hz, & 0° & 7.5° AoA
127
Figure B.12: Lift & Thrust vs. Phase at 5 m/s, 4 Hz, & 0°, 7.5° & 15° AoA
127
xii
LIST OF SYMBOLS AND ABBREVIATIONS
FL
Lift Coefficient
FD
Drag Force
CL
Lift Coefficient
CD
Drag Coefficient
CT
Thrust Coefficient
ω
Wing Angular Velocity
c
Root Cord Length
kFL
Reduced Flapping Frequency
θ
Pitch
AoA
Angle of Attack
xiii
SUMMARY
In this study a mechanism which produced flapping and pitching motions was
designed and fabricated. These motions were produced by using a single electric motor
and by exploiting flexible structures. The aerodynamic forces generated by flexible
membrane wings were measured using a two degree of freedom force balance. This
force balance measured the aerodynamic forces of lift and thrust. Two sets of wings with
varying flexibility were made. Lift and thrust measurements were acquired as the
mechanism flapped the wings in a total of thirteen cases. These thirteen cases consisted
of zero velocity free stream conditions as well as forward flight conditions of five meters
per second. In addition, flapping frequency was varied from two Hertz to four Hertz,
while angle of attack offsets varied from zero degrees to fifteen degrees. The four most
interesting conditions for both sets of wings were explored in more detail. For each of
these conditions, high-speed video of the flapping wing was taken. The images from the
video were also correlated with cycle averaged aerodynamic forces produced by the
mechanism. Several observations were made regarding the behavior of flexible flapping
wings that should aid in the design of future flexible flapping wing vehicles.
xiv
CHAPTER 1: INTRODUCTION
Over the past twenty-five years, interest in small-unmanned aerial vehicles
(UAVs) has greatly increased. Small UAVs range in size from the micro range, having a
wingspan of a few inches and weighing 80 grams, to the miniature range where they can
have spans up to 20 feet across and weigh up to 25 kilograms. Most of the UAVs in
production and use today are fixed wing airplanes. This means they employ traditional
methods of lift and thrust: a propeller for thrust and rigidly attached wings relying heavily
on the free stream velocity for lift. These vehicles are capable of performing wide range
of missions, having both military and civilian applications. These include surveillance,
communication relay links, decoys, and detection of biological, chemical and radiological
materials. However, there is another realm of UAVs that is just beginning to be explored,
those which utilize flapping wings. These types of vehicles are also known as
ornithopters.
The motivation for the development of an ornithopter is based on the argument
that flapping wing flight, at small scale, is more efficient than traditional fixed wing and
rotary flight [1]. Flapping wing flight more closely mimics natural flight and has
potential for being lower in weight and having greater endurance. In addition, strategic
and stealth applications for flapping wing vehicles are evident as well, as they mimic
natural flyers and could perch. Thus, flapping wing air vehicles may provide a
significant advantage over their fixed-wing counterparts [1].
Recent approaches involve analyzing bird, bat and insect flight [1]. This has led
to an increased understanding of the mechanisms that biological ‘machines’ which use
1
flapping to provide lift and thrust, but this knowledge has not readily transferred to a
machine analog. In analyzing natural flyers, the issue of wing flexibility has emerged,
with many insect and bird wings being complex elastic structures. It has been shown in
certain studies that the flexible nature of membrane type wings can actually increase
aerodynamic stability by damping unsteady forces and storing elastic energy [2]. While
some vehicles and mechanisms that utilize flapping wing flight have been demonstrated
[3], few have been successful. Furthermore, very little has been done to understand the
role of wing flexibility, and thus there is much more to be learned in this field.
The objective of this research was to design, construct, and test a small, low
inertia device capable of producing flapping and pitching that utilize flexible wings to
produce both lift and thrust. This device needed to provide plunging motions (pure
flapping) in addition to pitching motions and was to be powered by a DC micro-motor.
The device built in this stage was not designed to be a complete flapping wing robot
capable of sustained flight. Rather it was a mechatronic device which could provide a
suitable platform for measuring the forces of lift, drag and thrust. Cost was an issue due
to budget restrictions, so it was desired to build the flapping wing mechanism with as
many low-cost off the shelf materials as possible.
2
CHAPTER 2: LITERATURE SURVEY
It was mankind’s fascination with bird flight which originally spawned the
discipline of aerodynamics [2]. In the earliest stages of developing flying vehicles, it was
discovered that separating the mechanisms for lift and thrust was the easiest and quickest
way to become airborne, thereby freeing the earliest engineers from the fruitless attempts
at mimicking animal flight [3]. In the recent years an interest to imitating nature in the
development of UAVs has become more popular. Flapping wings have been thought to
be more efficient, maneuverable, agile and stealthier than fixed wings. Flapping is also
an interesting challenge in mankind’s quest to constantly imitate nature.
2.1
Lift Generation in Flapping Wing Flight
To begin to understand flapping wing flight, it is necessary to observe when lift is
generated during a flapping cycle. A typical cycle in the flight of a flapping wing vehicle
consists of a downstroke and an upstroke (Figure 2.1). Lift generation on the various
strokes of a flat rigid plate have been studied by Hong et al. [4]. Assuming the wing
starts from a maximum height position, at the start of the downstroke, the lift starts to
increase. Next is the actual downstroke, where the aerodynamic force peaks. Third is the
end of the downstroke, when the lift force starts to decrease. Next is the actual upstroke
where aerodynamic forces create negative lift as the wing travels upwards. At the end of
the upstroke where negative lift is generated again due to changing wind velocity
distributions along the wing’s surface [4].
3
Figure 2.1: Unit Force vs. Time for Up and Down Strokes [4]
Figure 2.2: Average Lift vs. Frequency [3]
It has been shown that the generation of lift is a fairly weak function of flapping
frequency (Figure 2.2) by DeLaurier et al. [3]. There is very little change in average lift
values as frequency increases. As the flapping frequency is increased, the amount of lift
generated increases slightly. With the above information, the lift force and the dynamics
4
can be characterized qualitatively, yielding a better understanding under what frequencies
to expect the maximum/minimum lift, and maximum/minimum acceleration during one
full stroke. This information was also useful in understanding when during a flapping
cycle lift generation could be expected
2.2
Thrust Generation in Flapping Wing Flight
In natural flyers, it has been shown that insects take advantage of unsteady
aerodynamic phenomena to generate thrusts [1]. The generation of thrust can be broken
into 4 parts [4]: First, on the downstroke the wing translates with a fixed collective pitch
angle, next near the end of the downstroke, the wing turns so that the blade angle of
attack is positive on the upstroke, third is the actual upstroke when the angle of attack is
still positive. Fourth is the end of the upstroke/beginning of the downstroke when the
wing’s angle of attack changes from positive to negative.
Figure 2.3 shows the lift and thrust generation with respect to the phase of a
flapping airfoil [5]. The wing starts at a point, labeled as 18°, and then proceeds to
complete one full flap (traveling 360°) and returning to its starting position. From Figure
2.3, it can be seen that thrust is almost always being generated, but positive lift forces
occur primarily on the down stroke.
Figure 2.3: Lift and Thrust Generation vs. Phase [5]
5
The generation of thrust is also a direct function of flapping frequency [3].
Delaurier et al. have shown that as the flapping frequency increases, so does the average
thrust generated. These results can be seen in the following graph:
Figure 2.4: Average Thrust vs. Frequency [3]
The above information was useful in understanding the effects of flapping
frequency on thrust generation as when to expect thrust forces during a typical flap.
2.3
Flexible Wings versus Rigid Wings
Since flapping wing UAVs fly typically at low Reynolds numbers, gusting and
disturbances in the flow are more problematic. It has been shown that flapping wing
based UAVs have certain advantages compared to their fixed wing counterparts: ability
to hover, react more efficiently to gusts, have lower weight, and generate lift without
excessive size and weight [8]. Flexible wings have also been shown to be more
advantageous than rigid wings, with having higher stall angles by performing adaptive
6
washout, and providing smoother flight [8]. In addition, every natural flyer has flexible
wings, and noting that nature converges towards the most efficient solution, it can be
believed that flexible wings are more advantageous than their rigid counterparts.
It is possible to replace the rigid surface of a wing with a more flexible membrane,
while still retaining the stiff structural members. This type of practice has been used for
centuries in ship sails, with a stiff mast providing the support while the sail is a
membrane material. It has been found that the main advantage of flexible wings is that
they facilitate shape adaptation, essentially adapting to the airflow to provide a smoother
flight [9]. It has been shown by Ifju et al. a wing changes shape as a function of angle of
attack and wind speed [8]. This adaptive washout is produced through extension of the
membrane and twisting of the structural members, resulting in angle of attack changes
along the span of the wing in response to the oncoming flow [9]. The shape change
causes a slightly decreased efficiency in lift, but because of gusting phenomena, the
overall lift is maintained. However, as the air speed decreases, the wing recovers to its
original position [9]. When there is a decrease in relative airspeed, the angle of attack of
the wing increases, and the wing becomes more efficient, resulting in near constant lift.
This enables a UAV with flexible wings to fly with exceptional smoothness, even in
gusty conditions.
2.4
Current UAVs and Flapping Wing Mechanisms
Since this thesis was concerned with designing a flapping wing mechanism, it was
useful to see what mechanisms already exist and typical designs (if any) are commonly
used. It was found that certain mechanisms were capable of flapping at higher
7
frequencies than others. The type of pitch motions varies between the mechanisms as
well; some can dynamically change pitch, while others have fixed pitch envelopes. Some
of the information learned from mechanisms designed by others was incorporated in
Chapter 4, which explains the design process of the mechanism for this thesis.
There are numerous small fixed wing UAVs in use today for a variety of
applications. Three of the more common fixed wing UAVs are the Dragon Eye [10],
Mite 2 [11], and Black Widow [12]. All three of these UAVs use traditional methods of
obtaining flight. They have flaps and rudders for directional controls and a propeller is
the main source of thrust. The propellers in these UAVs are powered by small battery
powered electric motors, and are capable for flying up to 60 minutes at speeds of up to 40
miles per hour depending on their size. There are also some UAVs which use miniature
jet engines to provide thrust.
Work has also been done on fixed-flexible wing UAVs. Ifju et al. [9] have
designed a series of flexible, fixed-wing UAVs (Figure 2.5) in an effort to determine the
role of wing flexibility in flight. Their basic structure and wingspan is similar to a small
aerial vehicle such as the Mite, and employs the use of a propeller to produce thrust. The
difference is that this mechanism has flexible wings. The wings are thin, un-cambered
and have been shown to be more efficient than those with significant thickness.
8
Figure 2.5: Flexible Wing UAV Developed at the University of Florida [9]
Various flapping wing mechanisms have been developed to measure aerodynamic
forces. Some have been capable of sustained flight [13], [14], [15] and [16].
Considerable efforts have been done to understand the nature of flapping rigid plates in
water [13]. This mechanism developed by Isaac et al., produced both dynamically
changing pitching and flapping motions. The main flapping was driven by a motor which
drove a flywheel with a connecting rod. The connecting rod was connected to the wing
through the use of a fixed pivot joint. Pitching motions were done through the use of a
servomotor. This motor was attached below the fixed pivot point so the entire motor
assembly was flapped as well, with the servomotor directly driving the pitch change of
the wing. This is one of the very few mechanisms which can produce controllable
changing pitching and plunging motions on the fly. The flapping frequencies used are
low, and the mechanism is flapped in water. Producing a mechanism which can produce
higher flapping frequencies and dynamically controllable pitching motions on the fly is a
significant challenge.
Mcintosh et al. [14] have been successful in creating a mechanism which is capable
of flapping two rigid wings while being able to change the pitching angle. This
9
mechanism has a distinct feature: both the pitching and flapping mechanisms are created
through the use of a single actuator. The motion created by this mechanism is similar to
many insects, wherein the wing is rotated at the top and bottom of each flap. Flapping
frequencies of 1.2 to 1.9 Hz could be generated. The drive mechanism is again a
connecting rod and gear assembly to produce the main plunging motions. Pitching
motion is generated through the use of various bending and torsion springs and a pin and
follower assembly. The mechanism varies its pitch during the flap. It is not controllable
on the fly, meaning the mechanism must be stopped and reconfigured to produce a
different set of pitching potions. An image of this mechanism can be seen in Figure 2.6.
Figure 2.6: Mechanism Capable of Biaxial Rotation [14]
The Microbat developed by Pornsin-Sirirak et al. [6] is a micro aerial vehicle
(MAV) with MEMS based membrane wings. These wings were made of titanium-alloy
(Ti6Al-4V) for the wing’s frame, and parylene C for the skin. The study mainly focused
on insect wings. A drive mechanism converting rotary motion to the flapping motion of
the wings was designed [15]. Figure 2.7 below shows a picture of the drive mechanism
used as well as a picture of the completed mechanism.
10
Figure 2.7: Microbat Transmission System and Fabricated UAV [15]
This design consists of a small DC motor with a 22:1 gearing reduction ratio
turning a geared flywheel which in turn drives a scotch yoke crankshaft in the vertical
motion. The crankshaft is restricted in motion so it can only move in the vertical
direction. This mechanism is capable of flapping at 42 Hz when no wings are attached,
and at 30 Hz with wings [15].
The largest successful flapping wing UAV designed is by DeLaurier et al. [3]. This
mechanism, like many of the others, converts rotational motion to translational motions.
A picture of this mechanism can be seen in Figure 2.8.
Figure 2.8: Drive Mechanism in Toronto Ornithopter [16]
The principle plunging motions are created by a motor. Through a series of
flywheels connected together by drive belts, a slider mechanism is driven in an up and
11
down motion. The slider assembly is connected to two parallel posts which move up and
down. The two posts raise and lower a center section of wing. This section is in turn
connected to the left and right wing in a hinge like connection. The wings are held in
place through a type of pivot joint and when the center panel is raised and lowered
through the use of the slider assembly, the left and right wing are caused to plunge
because of the pivot joint. Frequencies from 3 Hz - 5 Hz have been generated by this
mechanism [16]. This flapping wing mechanism has been successful in actual sustained
flight and is perhaps the most successful flapping wing mechanism to date.
2.5
Wing Geometries of Natural Flappers
Part of this research involved designing a flexible wing to be used in the flapping
experiments, and therefore was helpful to observe the various types of wings natural
flyers have developed. Based on the information found on wing geometries of natural
flyers, a decision could be made as to which one to imitate in this thesis. Birds, insects
and bats were studied. Once a particular natural flyer was selected, the wings could be
studied in more detail, and a simplified version could be constructed for testing purposes.
Avian wings were the first kinds of wings studied in the quest to design flight
vehicles [17]. In designing wings for fixed wing aerial vehicles engineers used relatively
thin airfoils, as those found in birds. Studies conducted on a seagull wing have shown
that the wing has two regions of different flexibilities. The wing consists of a stiffer
section closer to the root, and has higher flexibility closer to the tip [17], [18]. The
ornithopter developed by DeLaurier employs this avian model in the wing design [5].
12
Insects and bats both have membrane wings. The wings of an insect are very thin
and various veins make up the members for structural rigidity [19]. Their wings are
predominantly oval in shape and extremely flexible. It was found that insect wings
would be extremely difficult to reproduce. Bat’s wings on the other hand are slightly
different. They have approximately 5 main structural members known as battens, though
their flapping motion is different from both birds and insects [20]. Research has been
done by Tian et al. on the kinematics of bat flight. Figure 2.9 below shows images of the
motion a bat wing produces in addition to showing the locations of the structural
members.
Although the flapping motions produced by the bat were not reproduced in this
thesis, the planform and locations of the structure was. The bat wings were chosen over
insect and bird wings because they met two important criteria: they were membrane
wings, and were relatively easy to reproduce. The basic form and location of the
members was copied, with complex curved features being simplified by being made
linear wherever possible. This is further discussed in Section 4.5.
Figure 2.9: High Speed Video of Bat Wing [20]
13
2.6
Missing Links in Current Research
Research efforts have been done in hopes of understanding why flapping wing
flight is beneficial and more efficient. It has been shown that natural flyers are capable of
performing a broader range of missions than their fixed wing counterparts. In addition,
studies on flexible wings have proved that they are more resistant to stalling at higher
angles of attack and produce the same amount of lift as rigid wings, all the while
providing smoother flight and better gust stability using adaptive washout.
Various flapping mechanisms have been constructed which flap wings, flexible
and rigid, at different frequencies. Additional mechanisms have also been built where
rigid wings are flapped where there is dynamic pitch and amplitude control. These
experiments have been conducted in water, and the flapping frequencies are very low,
allowing the motors which control both degrees of freedom to work together more easily.
Currently, the only mechanisms which alter pitch do so in direct drive forms, meaning the
rates of pitch change and deflection of the pitch angles are constant for a given frequency.
To the author’s knowledge, at this time, there is no mechanism which flaps thin
membrane wings and is able to determine the aerodynamic forces generated at different
frequencies. There is also no clear understanding on how the flexibility of membrane
wings affects lift, drag and thrust in flapping flight. To explore these open concerns and
questions, this research aims to develop inexpensive hardware that produces pitch and
flapping motions that could lead to future UAV applications.
14
CHAPTER 3: MECHANICAL DESIGN REQUIREMENTS
3.1
Objective
The objective of this research was to design a flapping wing mechanism which
could produce both flapping and pitching motions. In designing this mechanism, the
most important factors were weight, wing design, flapping frequency and flow velocity.
Cost was also a major issue, and it was desirable to keep it to a minimum. This meant
using commercially available off the shelf parts wherever possible.
3.2
Weight Requirements
Due to the fact that this mechanism was to simulate a flapping wing aerial robot, it
was necessary to be as light weight as possible. Each component and sub-assembly was
weighed and an effort was made to choose light-weight materials. The mechanism was
built to emulate a larger bird in size, such as a crow. The crow was chosen as a weight
and size (wingspan) target. It was found that the weight of a crow is approximately 1.5 to
1.75 pounds [21], thus it was desirable that all of the parts combined did not weigh more
than this. Parts such as motors, bearings and joints constitute a significant amount of
weight, so it was necessary to choose materials which had very low cost-to-weight ratios.
3.3
Wingspan and Planform Requirements
Larger birds and bats have wing semi-spans of approximately 16 inches [21].
Since the mechanism had a target weight to that of a crow and a large bat, it was also
15
desirable to have the same wing span as a large bat or crow. Since the wing was
supposed to be a membrane wing, the largest natural flapper which employed this
characteristic is a bat, and therefore the wings were designed to be like those of a bat.
This involved having structural members, or battens, in the same places a real bat does as
well as using a thin membrane. Structurally, the wing needed to be stiff at the leading
edge, while having a very flexible membrane.
Figure 3.1: Planform of a Bat’s Wing Showing Structural Members [22]
3.4
Flapping Frequency and Speed Requirements
Analysis of bird and insect flapping motions show that sustained forward flight can
be produced by different flapping motions, and that the motion appropriate for one
vehicle or one wing might not be the best for another wing or vehicle. Crows have a
flapping frequency of approximately 4 Hz or wing-beats per second [21]. This meant
that the target flapping frequency for the flapping mechanism had to be at least 4 Hz,
with the possibility at flapping at a higher frequency being desirable. It was decided to
flap the mechanism at 2, 3 and 4 Hz, at various free stream velocities. 10 Hz was
arbitrarily chosen as an upper bound in frequency when selecting a motor. Realistically,
16
large natural flappers do not flap at frequencies as high as 10 Hz, but it was thought it
might be interesting to observe how the mechanism behaved at higher frequencies.
According to Figure 3.2, it can be seen that the cruising speed of natural flappers
which have a mass of approximately 1.5 lbs to 1.75 lbs is approximately 10 to 13 m/s.
However, the flapper must also experience speeds below this, so a target speed of 5 m/s
was chosen. This enabled testing at speeds of 0, 5 and 10 m/s to more fully understand
the nature of flapping. Therefore, it was necessary that the wind tunnel facilities be able
to reach speeds as low as 5 m/s.
Figure 3.2: Flight Speed of Flyers vs. Mass [6]
3.5
Summary of Requirements
Table 3.1 lists the desired design requirements for the flapping mechanism.
Table 3.1: Target Design Requirements
Desired Weight:
≤ 1.75 lbs
Desired Wing Semi-Span:
16 in.
Desired Flapping Frequency:
0 ≥ f ≤ 4 Hz
Air Velocities:
0, 5, 10 m/s
17
CHAPTER 4: DESIGN PROCESS
4.1
Mechanism
A complete set of CAD models were developed to ensure an accurate fit between
parts. The software used to generate CAD models was SolidWorks 2005. An isometric
conceptual view of the flapping mechanism can be seen in Figure 4.1. This figure also
depicts the relative scale between the flapping mechanism and the wings
Figure 4.1: Isometric View of Entire Flapping Mechanism (CAD Model)
18
Top and left side views can be seen in Figure 4.2, and Figure 4.3. A DC Micro
motor/gearhead assembly was face-mounted to a motor mounting plate (Figure 4.2,
Figure 4.3).
Right
Flapping
Shaft
Right Swivel
Bearing
Flywheel
Flexible Helical
Coupling
Right-Side Wall
Motor Mount
Linear
Bearing
Mount
DC Micro motor
Top
Linear
Bearing
Base Mounting
Plate
Left
Flapping
Shaft
Left-Side Wall
Left Swivel
Bearing
Crankshaft
Main
Drive
Shaft
Ball Bearing
Mounting Plate
Figure 4.2: Top View of Flapping Mechanism (CAD Model)
The output shaft of the motor was connected to a helical beam coupling, which
was connected to a main drive shaft. A helical beam coupling was chosen to ensure the
elimination of any shaft misalignment. The coupling chosen was capable of correcting
for up to 1.5° of shaft misalignment. The drive shaft passed through a ball bearing for
additional support. This ball bearing was press-fit and housed within the ball bearing
mount. The far end of the main drive shaft was connected to a flywheel through the use
19
of a set screw. A setscrew was used because it was very low profile and flush with the
surface of the flywheel when fully tightened; more importantly it was very low mass.
Linear
Bearing
Mount
Top
Linear
Bearing
DC Micro motor
Bottom
Linear
Bearing
Motor Mount
Crankshaft to-Flywheel
Pin
Main Drive
Shaft
Crankshaft
Flywheel
Flexible Helical
Coupling
Ball Bearing
Mount
Figure 4.3: Left Side View of Flapping Mechanism (CAD Model)
The flywheel was used to enhance the inertia of the system. Equation 4.1 was
used to estimate the torque due to the system’s increased inertia.
τ = Iα
Equation 4.1
First it was necessary to calculate the moment of inertia of the flywheel, I. This
was given by Equation 4.2.
20
I=
1
mr 2
2
Equation 4.2
In this equation, the mass was taken to be 0.02 kg, the radius r was 0.0191 m, and
therefore, the calculated value of I was 3.6x10-6 kgm2. From the specification sheets of
the motor, the maximum angular acceleration α, of the motor was 120x103 rad/s2. Using
a 14:1 planetary gearhead, this was reduced to 8.57x103 rad/s2. Substituting the values
into Equation 4.1, the increased torque was calculated to be 2.38x10-3 Nm.
Equation 4.3 was used in determining if the motor had enough torque to flap the
wings. In Equation 4.3, τ is the motor torque, r is the torque arm, and F is the force the
motor needs to be able to lift. The radius was measured to be 5.25 inches (0.1334 m),
which was the distance from the center of the crankshaft to the pivot point at the swivel
bearings. The weight of the wing was measured to be 0.02 kg.
τ = r×F
Equation 4.3
τ = 0.1334m × 9.8 m s 2 ⋅ 0.02kg = 26.1mNm
Equation 4.4
From Equation 4.4, it can be seen that the minimum torque required to lift the
wing from the bottom position of the flap, to the highest point in the flapping motion is
26.1 mNm. Since there are two wings, the required torque is 52.2 mNm. Since the motor
selected only has a specified torque of 10 mNm, a gear head was needed to increase the
torque. The highest frequency expected in the flapping motions was approximately 10
Hz, so it was not necessary to flap faster than that.
To achieve both of these requirements, a planetary gear head was chosen. A planetary
gear head was chosen over a spur gear head because they produce higher torque in a
21
limited space, whereas spur gear heads typically consume less power but are larger and
heavier. To achieve speeds of 10 Hz, or 600 RPM, Equation 4.5 was used. In this
equation, ω is the desired speed, ωNL is the no load speed of the motor and RG is the
reduction of the gear head. Equation 4.6 solves for the desired reduction. It can be seen
that the reduction ratio needs to be approximately 13.33:1.
ω=
ω NL
RG =
Equation 4.5
RG
8000rpm
= 13.33
600rpm
Equation 4.6
A coreless DC micro motor (model number 2232) was purchased from Faulhaber
Micromo Electronics. The speed versus torque curve can be seen in Figure 4.4 [24]. It
was a 12 volt DC coreless micromotor, with a maximum rpm of 8000 and a current rating
of 2.7 amps. Coreless motors are lighter than traditional DC motors and as such are more
commonly used in aerospace applications. The closest gear head available which fits the
2232 motor was a 14:1 reduction. This yielded a new speed of 571 RPM, or 9.5 Hz. To
calculate the torque increase due to this gear head, Equation 4.7 was used. In this
equation τNew is the torque at the output shaft of the gear head, τOrig is the original torque
at the motor shaft, and ε is the efficiency of the motor.
τ New = τ Orig ⋅ RG ⋅ ε G = 10mNm ⋅ 14 ⋅ 0.9 = 126mNm
22
Equation 4.7
Thus, using a gear head reduction ratio of 14:1, the motor speed was reduced to 9.5
Hz, and the torque was increased to approximately 128.4 mNm including the effects of
the flywheel. This was enough torque to successfully flap the wings.
This is a very rough estimate, since there is drag faced by the wing surface as it
moves up and down. This additional force should be accounted for. However at the time
of motor selection, there was no information about the types of forces generated when
flapping flexible wings. It would be necessary to take into account the flexure of the
membrane and the resulting drag force at that frequency. Most of these were unknown at
this time, and these are the questions this thesis is attempting to answer.
Figure 4.4: Speed vs. Torque Curve for 2232 Micromo Motor [24]
23
The model 2232 motor was purchased because it offered a very good tradeoff
between weight and power. It weighs only 62 grams, while being able to provide 10
mNm of torque at 8000 rpm.
Right
Flapping
Shaft
Crankshaftto-Flapping
Shafts Pin
Crankshaft
Flywheel-toCrankshaft
Pin
Left
Flapping
Shaft
Flywheel
Figure 4.5: Close-Up View (Top) of Drive Mechanism (CAD Model)
The flywheel has an Oilite® bushing press-fit into it (Figure 4.6), through this
passes the “flywheel to crankshaft connecting pin”. The pin is held into place by the use
of an external retaining ring. An Oilite® bushing was used because it was lower cost and
lower weight alternative to a standard roller bearing, which would have been used, had
rotation speeds been high. These bearings are oil impregnated and lubricate the shaft to
lower the coefficient of friction between the shaft and the bearing inner race as the shaft
24
rotates. The other end of the pin is press-fit into a ball bearing (Figure 4.6), which itself
is press-fit into a hole in the crankshaft.
Crankshaft
Ball Bearing
Crankshaftto-Flapping
Shafts Pin
Flywheel
Oilite
Bushing
Flywheel-toCrankshaft
Pin
Figure 4.6: Close-Up of Flywheel and Crankshaft Connecting Pins (CAD Model)
The top end of the crankshaft has another ball bearing press-fit into it (Figure
4.6). Through this ball bearing passes the “crankshaft-to-flapping shafts pin, again pressfit into the second ball bearing. The two flapping shafts (left and right), have male and
female connection joints which allow them to mesh within themselves. Each side has a
hole, through which the “crankshaft-to-flapping shafts pin” passes. The far end of this
pin is held in place through the use of a shaft collar. Originally, retaining rings were used
for this connection, but the loads produced by the flapping wings caused the retaining
rings to squeeze loose. The external retaining rings for 1/8 inch diameter shafts were
25
originally used because of their almost negligible weight (0.001 mg). The retaining rings
were replaced by the above mentioned shaft collars after the first test.
Through these series of connections, as the motor rotates, so does the crankshaft.
This in turn causes the flywheel to rotate. As the flywheel turns, the ball bearings allow
the crankshaft to move up and down, essentially converting rotary motion to linear
motion. In order to get this linear up and down motion to convert into a plunging,
flapping motion, swivel joints are used. These swivel joints are press-fit into each wall
Figure 4.7. As the crankshaft moves up and down, one end of each flapping shaft is
forced to translate up or down. The flapping shaft passes through the side wall, and thus
the swivel bearing. This enables the shaft to pivot about the side wall and perform
plunging motions. To keep the crankshaft to stay true in the center of the mechanism and
not travel side to side, two springs were compressed-fit between the side walls and the
roller bearing housing.
To allow for pitching motions, two approaches were taken. First, a ball
bearing/housing assembly was used (Figure 4.7). The inner race of the bearing was press
fit over the far end of each flapping shaft. The outer race was press fit into a housing
(Figure 4.7), the far end of which connected to a wing shaft via the use of a shaft
coupling (not shown). This enabled the wings to rotate freely. An actual image of this
can be seen in Figure 4.7.
26
Wing Shaft
Swivel Joint
Flapping
Shaft
Roller
Bearing
Housing for
Pitching
Control
Roller
Bearing
Figure 4.7: Close-Up of Swivel Joints and Pitching Assembly (CAD Model)
The second approach for producing pitching motions involved natural properties
of the wing materials. To do this, additional wing shafts were fabricated which did not
utilize the roller bearing and roller bearing housing. These shafts were designed for pure
wing plunging, with no pitch control. The pitch control for this direction was taken into
account when fabricating the wings, with natural material frequency modes providing the
necessary pitch when the wings were flexed. Chapter 4.5 further discusses the flexible
wings with natural pitching exhibited through the wing structural material’s stiffness.
Real-life images of the flapping mechanism can be seen in Figure 4.8 through Figure
4.11.
27
Figure 4.8: Isometric View of Flapping Device
Figure 4.9: Top View of Flapping Device (Without Motor and Coupling)
28
Figure 4.10: Front View of Flapping Device
Figure 4.11: Close-Up View of Swivel Joints After Weight Reduction Efforts
4.2
Materials and Dimensions Used
In order to standardize the assembly process, all major tapped holes were size #8-
32. The base plate, left and right side walls were made of 3/8 inch polycarbonate. The
base plate was 5 inches long and 3 inches wide. The left and right walls were each 5
inches long and 4 inches wide. It was found that these were the minimum dimensions
29
which would provide enough room for the mechanism drive-train. All of the bearing
mounts (for both linear and ball) as well as the motor mount were machined from
Aluminum 7075-T6. This alloy was chosen because it is a very light weight aluminum
alloy with excellent machineability characteristics. It is also widely used in aerospace
applications. The flapping shafts, flywheel, crankshaft and the roller bearing housings
for pitching were all also machined from the same alloy. The flapping shafts were 2.75
inches long made of 0.25 inch diameter aluminum, and the crankshaft was 2.098 inches
long.
The drive shafts as well as the two pins were all made of 1/8 inch titanium.
Titanium was chosen because it is stronger than aluminum and lighter than steel. These
parts felt the brunt of the loads in this mechanism and thus, it was necessary to ensure
adequate strength.
The linear bearings, ball bearings and swivel joints were all steel with press-fit
actions used wherever possible. When necessary, the press-fit application was
augmented with the use of Loctite epoxy for an extra firm hold. All materials were
purchased from McMaster-Carr.
4.3
Mechanism Electronics
In order to get an accurate reading of the flapping frequency, an optical encoder
was used (Figure 4.12). The optical encoder wheel was purchased from US Digital. The
optical encoder was chosen with a hub assembly to facilitate mounting on a shaft. It was
designed for a 0.125 inch shaft and held in place with a set-screw. This encoder wheel
was mounted on the 0.125 inch titanium drive shaft. The encoder wheel chosen has a
30
resolution of 500, meaning there are 500 holes at an optical radius of 0.433 inches. In
order to properly read the counts on the encoder wheel, an optical encoder module was
used. This module had a two channel quadrature output with index pulsing. The encoder
module has an emitter-detector feature. The module emits a light, and as the encoder
wheel spins, one of the windows passes over the emitter allowing the light to be detected
by the detector. This constitutes one count.
Figure 4.12: Encoder Hub Disk and Module Used
4.4
Weight Reduction Efforts
As stated earlier, light weight materials were chosen for the design. These included
using aerospace grade aluminum alloys, polycarbonates and titanium wherever possible.
In an effort to further reduce weight, parts a post processing step which involved
removing material by hand was performed. This involved removing material wherever
possible. Figure 4.13 displays an isometric view of the entire mechanism after weight
reduction efforts were completed.
Two sections of the linear bearing mount were machined down from 0.25 inches
to 0.125 inches, and 24, 0.25 inch holes were drilled through it (Figure 4.14). The left
and right side walls, as well as the base plate had 0.5 inch holes drilled through them, for
a total of 12 holes per side. The linear bearing mount also had 0.25 inch holes drilled
31
through it; in addition 2 sections of the 0.25 inch thick material was reduced to 0.125
inches. All machining was done on a 3-axis Bridgeport milling machine.
Figure 4.13: Isometric View of Mechanism After Weight Reduction Efforts
Linear
Bearing
Mount
Linear
Bearing
Figure 4.14: Top View of Mechanism After Weight Reduction Efforts
32
Table 4.1: Table of Mechanism Weights Before and After Weight Reduction Efforts
Weight After Weight
Part/Assembly
Original Weight: g (lb)
Reduction: g (lb)
Motor + Gearhead
128 (0.28)
128 (0.28)
Left side wall (w/ swivel joint)
146 (0.32)
120 (0.26)
Right side wall (w/ swivel joint)
146 (0.32)
120 (0.26)
Base plate (w/ linear bearing)
176 (0.38)
160 (0.35)
Motor mount
66 (0.14)
66 (0.14)
Ball bearing mount (w/ ball bearing)
68 (0.15)
46 (0.10)
Flywheel/crankshaft/connecting pins
45 (0.10)
45 (0.10)
Ball bearing housing (w/ bearings) x2 14 x2 (0.03 x2)
14 x2 (0.03 x2)
Top linear bearing mount (w/ bearing) 128 (0.28)
90 (0.20)
Weight of wings
16 x2 (0.035 x2)
16 x2 (0.035 x2)
Total Weight
963 (2.12)
839 (1.82)
Table 4.1 displays the weight of the mechanism parts and sub-assemblies before
and after weight reduction. Target design requirements from Table 3.1 call for the
mechanism to weigh approximately 1.75 lbs, and the weights after weight reduction fall
very close to the target range. An effort was made to use the lightest available materials.
However, due to budget restrictions only materials available on hand were used, such as
aluminum and polycarbonate. It would definitely be possible to achieve a weight less
than 1.75 lbs, but this would increase cost which was a major factor in this experiment.
4.5
Wings
One of the most important aspects of this effort was wing design and development.
This research called for flexible membrane bat wings. As discussed in Section 3.3 and
Table 3.1, the wings each needed to have a semi-span of 16 inches. Since the mechanism
was designed to emulate a natural flapper the size and weight of a crow, a crow’s
33
wingspan was chosen, while the structural members and supports of a bat’s wings were
copied (Figure 3.1).
4.5.1
Wing Fabrication Process
Two families of wings with varying stiffness were used. The first wing was
classified as “flexible”, while the second was relatively more rigid or “semi-rigid”. Tests
were performed on the “flexible” wing, labeled as Wing 1. Eventually, high speed video
imagery was taken to observe its behavior. After the behavior was studied, a second
“semi-rigid” wing was made.
The wings were made from three materials: fiberglass, carbon fiber and epoxy.
The skin of the wing was made from two layers of fiberglass, each 0.0025 inches thick
(post-cured). The structural members consisted of carbon fiber braided sleeves filled
with fiberglass unidirectional strands. The manufacturing process of the wings was very
straight forward. A right side and left side mold was fabricated from 0.25 inch thick
aluminum 6061 (Figure 4.15). These molds were mirror images of each other.
Aluminum was used because it would not bend or warp over time and is very durable.
Each mold was 9 x 18 inches to allow for a wing of appropriate size. Both sides of the
mold had channeled grooves. These grooves were in the same location where the
structural members should be. There was a main spar groove which ran from the wingtip
to the root. Three additional grooves were cut from each of the other tips, and joining the
spar groove at various locations.
The fabrication process for the first set of wings is as follows: one carbon fiber
sleeve was placed in the main spar groove from the tip to the root of the wing.
Successive sleeves were placed from each of the other three tips all the way to the wing’s
34
root. This divided the wing into four sections. The layering of the carbon fiber strands in
this manner meant that the sections of the spar closer to the wing’s root had more layers
and strength than those sections closer to the wingtip. Four strands made up the
structural member fit into an aluminum shaft coupling which was attached to the main
flapping shafts. The carbon fiber and fiberglass were saturated with epoxy. Both molds
were placed in a vacuum bag for curing. The vacuum bag provided pressure to compact
the laminate providing good consolidation and inter-laminar bonds while also providing a
vacuum to draw out volatiles and trapped air, resulting in a low void content wing. The
vacuum bag also helps to improve resin flow while the laminate cures.
This second stiffer wing was made by using larger diameter carbon fiber sleeves
(0.3 inches instead of 0.1 inches) as structural members from the wing’s root to the
wingtip. 0.1 inch sleeves, filled with fiberglass unidirectional, were still used for the
other structural members, only the leading edge was strengthened. This 0.3 inch diameter
sleeve ran from the wing’s root to the tip and was filled with both fiberglass as well as the
carbon fiber sleeves which provided strength to the other structural points. So essentially
this 0.3 inch sleeve was bundled and filled with 0.1 inch diameter unidirectional filled
carbon fiber sleeves, as well as additional fiberglass leading out to the wingtip. One of
the completed wings can be seen in Figure 4.16.
The radii on the joint corners of the mold were approximately 0.1875 inches. The
larger diameter carbon fiber sleeves had a more difficult time staying in place during the
curing process as they rounded these corners. For this reason the corner radii were
increased to 0.375 inches for the semi-rigid wings.
35
Figure 4.15: View of Wing Mold – One Half (CAD Model)
4.5.2
Wing Flexibility
After each set of wings were built, it was useful to determine how much the wings
would deform, or flex, under an applied load. This would allow for a quantization of the
wing’s flexibility characteristics. This testing was performed in two parts. First, various
loads from 0 to 50 grams were applied to each of the major 7 intersection and connection
points on the structural skeleton, with the resulting deformation being measured. The
second test involved making sure the wing could handle a load of 1 lb without failing. 1
pound was selected as a target because the entire apparatus weighed approximately 1.75
lbs, with two wings distributing the load between them at about 1 lb each.
To perform the first test, the wing was clamped at the root to a table edge with its
membrane parallel to the horizontal surface. The wing was categorized into 7 structural
points, with each point being assigned a number from 1 to 7. Figure 4.16 below shows
36
the locations of the 7 points. The black lines are the unidirectional filled carbon fiber
sleeves. The white is the fiberglass membrane.
7
6
5
1
2
3
4
Figure 4.16: 7 Structural Points of Flexible Wing 1
At each of the 7 locations, individual weights were placed, ranging from 3 grams
to 50 grams. A laser distance measurement tool was placed on the ground under the
wing, which was clamped to the edge of the table. The laser was first aimed at the
underside of point 1 (Figure 4.16), and the initial position was recorded. Next, a 3 gram
weight was added to the top of point 1; this caused the wing to deform slightly. The laser
measurer was then used to record the new position, which was the amount of deflection.
This result was subtracted from the initial measurement yielding a true value of
deflection. Then additional weights were added to point 1, with the deflection of each
being measured. This process was done for each of the 7 structural points of the wing.
Table 4.2 lists the weights used and the amount of deflection at each point.
37
Table 4.2: Weights Applied to Structural Points of Wing 1
Weight (lb)
Point 1
Deflection
(in)
Point 2
Deflection
(in)
Point 3
Deflection
(in)
Point 4
Deflection
(in)
Point 5
Deflection
(in)
Point 6
Deflection
(in)
Point 7
Deflection
(in)
0.0066
0.011
0.022
0.044
0.066
0.088
0.11
0.228
0.396
0.804
1.5
2.22
3.33
5.244
0.144
0.276
0.456
0.888
1.284
1.908
2.508
0.06
0.096
0.168
0.264
0.432
0.54
0.684
0.036
0.06
0.132
0.204
0.288
0.408
0.492
0.024
0.048
0.06
0.096
0.132
0.144
0.156
0.024
0.048
0.084
0.132
0.18
0.276
0.324
0.072
0.132
0.216
0.336
0.492
0.648
0.84
Applying the weights in steady increments allowed for the observation of the
wing flexibility. From the above table, it can be seen that majority of the deflection
occurs towards the tip of the wing. This is as one would expect since in natural flyers,
the area nearest the wingtip deforms the most. In natural flyers, most of the lift is
generated farther away from the root of the wing. This is due to the high amount of
deflection the wingtips see from a rest horizontal position. Figure 4.17 below shows a
plot of the applied loads at each point and the resulting deflections.
38
Figure 4.17: Wing 1 Stiffness Curves
The second step was to ensure that the wings were capable of supporting the load
of the mechanism without failing. The entire mechanism weighed approximately 2 lbs,
and since there were two wings, each needed to be capable of lifting 1 lb. To test this, a
similar test procedure was developed as with the previous wing deflection experiment.
This time however, each of the 7 structural connection points was loaded at the same time
with 1 lb of weight. This was done in 3 trials. In each trial, the load was distributed
among those 7 points. Table 4.3 displays each of the 3 trials and the loads applied at each
position. After all of the weights were applied on the wing, the laser measurement tool
described above was used at each point to calculate the resulting deflection. This value
39
was subtracted from a preliminary initial position value to give a true deflection amount
for the applied weight.
Table 4.3: Distributed Loading on Flexible Wing
Position
1
2
3
4
5
6
7
Trial 1
Deflection
Weight (lb)
(in)
0.044
0.791
0.11
0.811
0
2.508
0.22
1.524
0.44
0.564
0.11
1.896
0.066
2.988
Trial 2
Weight Deflection
(lb)
(in)
0
0.618
0.066
0.711
0.11
2.748
0.11
0.336
0.44
0.612
0.22
1.788
0.044
2.604
Trial 3
Weight Deflection
(lb)
(in)
0
0.625
0.044
0.703
0.066
2.604
0.22
2.112
0.44
0.564
0.11
1.752
0.11
2.796
From the above table, it can be seen that even though the positions of the loads
were changed, the amount of deflection is quite consistent for the amount of weight
added. Since the wing did not fail during these experiments, it is safe to assume that it is
capable of carrying a load of 1 lb.
The same experiment was carried out for the second and stiffer Wing 2. Since the
wing was stiffer larger weights were used (Table 4.4).
Table 4.4 Weights Applied to Structural Points of Wing 2
Weight (lb)
Point 1
Deflection
(in)
Point 2
Deflection
(in)
Point 3
Deflection
(in)
Point 4
Deflection
(in)
Point 5
Deflection
(in)
Point 6
Deflection
(in)
Point 7
Deflection
(in)
0.11
0.22
0.33
0.44
0.55
0.66
0.77
0.88
0.99
1.1
0.384
0.72
1.14
1.764
2.34
2.808
3.072
3.828
3.852
4.248
0.3
0.516
0.864
1.308
1.596
1.824
2.064
2.412
2.724
3.036
0.108
0.18
0.288
0.468
0.636
0.756
0.936
0.996
1.044
1.164
0.168
0.204
0.264
0.348
0.444
0.564
0.624
0.696
0.792
0.9
0.036
0.06
0.072
0.072
0.096
0.096
0.12
0.144
0.168
0.216
0.12
0.18
0.24
0.312
0.408
0.468
0.504
0.552
0.6
0.672
0.168
0.288
0.384
0.492
0.588
0.72
0.828
0.936
1.02
1.14
40
Figure 4.18 below shows a plot of the applied loads at each point and the resulting
deflections.
Figure 4.18: Wing 2 Stiffness Curves
Table 4.5 below shows the increase in stiffness of each point from Wing 1 to
Wing 2. It can be seen that there is a dramatic increase in stiffness for each point.
Table 4.5: Stiffness Increases from Wing 1 to Wing 2 per Point
Point:
Wing 1 Stiffness (lb/in):
Wing 2 Stiffness (lb/in):
Increase in Stiffness %:
1
0.0978
4.1064
41.9852
2
0.0487
2.7722
56.8824
3
0.0131
1.1359
86.8670
41
4
0.0096
0.7610
79.6400
5
0.0028
0.1587
57.2393
6
0.0063
0.5567
88.8723
7
0.0156
0.9792
62.7998
The point which saw the greatest increase in stiffness was Point 6, followed
closely by points 3 and 4. When the first wing was cantilevered, and had weights applied
to it, Point 6 was the point where the wing always buckled. This gain in stiffness at this
point was very beneficial and dramatically increased the structural stability of the wing.
42
CHAPTER 5: EXPERIMENTAL APPARATUS
5.1
Force Balance
A testing apparatus was constructed to measure lift and thrust forces generated by
the flapping mechanism. The test bed was essentially a set of springs coupled with linear
ball bearings and linear air bearings. A testing superstructure frame built out of 1 inch
aluminum structural tubing was constructed to route wires and mount mechanism
electronics. A conceptual view can be seen in Figure 5.1.
Testing
Superstructure
Center TConnectors
Base
Connectors
Flapping Mechanism
Linear
Transducer
Base
Plate
Corner
Connectors
Linear Air
Bearing
Figure 5.1: Test Superstructure and Flapping Mechanism (CAD Model)
43
The basic premise of this testing superstructure was to use springs, linear position
transducers, and bearings in parallel to measure distance and thrust. The mechanism was
constrained by bearings so that it was only capable of motion in the X and Y directions
(Figure 5.1). Motion in the +X direction represented thrust, while motion in the –X
direction represented drag. Similarly, motion in the +Y direction represented lift. Figure
5.2 below shows a close-up view of the mechanism’s ability to translate ±Y.
In order to move in the X direction, a linear air bearing was used. Originally,
linear ball bearings were used in conjunction with a rail assembly on which they rode.
However, this idea was not used because the static friction inherent in the ball bearings
was too high, and there were also binding issues. The air bearing was supplied with 90
psi, and yielded an almost frictionless cushion of air for the mechanism to move on.
Connected to the air bearing was an aluminum bracket (Figure 5.3). The mechanism
itself was mounted directly to this bracket via the use of an aluminum rod.
When the measuring end of the linear transducers was connected to the
mechanism, the 7 ounces of force their internal spring had was enough to move the
mechanism all the way to one end. This was due to the recoiling force required to keep
the measurement cable in constant tension. To constrain the mechanism at the center
point of the air bearing, a spring was used. One end of the spring was attached to the
sliding part of the air bearing, while the other was attached to a fixed point on the testing
apparatus. This distance where the fixed-end of the spring was attached was hand
calibrated until the mechanism naturally stayed in the center point of the air bearing,
using the spring force as well as the linear transducer’s recoil force.
44
The mechanism rode up and down in the ±Y direction on this rod through the use
of 2 linear ball bearings (Figure 4.2). As shown in Figure 4.2, these bearings were
mounted directly to the flapping mechanism. The mechanism was suspended on the
center of the rod through the use of springs (Figure 5.2). Since springs were placed in
parallel to the bearings’ direction of translation, the mechanism created motions in the ±X
and ±Y directions. The distance the mechanism moved was measured with the position
transducers. These transducers, in turn with known spring constants of the springs,
yielded force measurements.
Center Shaft
Stopping Cap
Springs
Linear
Transducer
Center Shaft
Figure 5.2: Close-Up of Linear Bearing Housing Assembly (CAD Model)
45
Air
Bearing
Mounting
Bracket
Input for
Pressurized
Air
Linear
Transducer
Air Bearing
Figure 5.3: Close-Up of Mechanism on Center Shaft (CAD Model)
A metal frame was built around the edges of the test bed. This frame was build
using 1 inch aluminum structural tubing. The tubing was connected using 3-exit corner
fittings as well as base-joint fittings, as shown in Figure 5.1. This frame served two
purposes. First, it gave a base to mount the linear transducer measuring ±X direction
motions, as well as a mounting fixture to mount a terminal block which was used in
wiring the mechanism electronics (i.e. motor, encoder, transducers). The aluminum
tubing was also served as a wire routing frame to neatly hold and run wires from the
mechanism and all of its electronic components to the LabView data acquisition cards
and control computer. Neatly routing the wires and securing them to a frame ensured that
the wires would not get tangled, or tear at connection joints while transmitting data to a
computer more than 10 feet away from the mechanism. An actual image of the testing
assembly can be seen in Figure 5.4.
46
Figure 5.4: Actual View of Mechanism in Test Assembly
5.2
Springs
In order to keep the mechanism centered within the testing structure, a series of
springs were used. These springs were purchased from Century Spring Corp, and W.B.
Jones Spring Co. Table 5.1 below shows the springs used and their various properties.
Spring 3 was a custom made spring purchased from W.B. Jones Spring Co.
Table 5.1: Summary of Springs Used for Centering Mechanism in Test Apparatus
Outer Diameter Inner Diameter
Free Length
Spring Constant
Spring #
(in)
(in)
(in)
(lb/in)
1
0.640
0.570
11.0
0.280
2
0.687
0.563
16.0
1.60
3
1.250
1.100
11.0
0.250
47
To keep the mechanism suspended in the vertical direction (± Y), a combination
of Spring 1 and Spring 2 were used. Spring 1 was used above the mechanism and Spring
2 was used below it. Spring 2 was a stiffer spring because it also needed to support the
weight of the mechanism. Now that the mechanism was constrained between 5 springs
(3 mentioned in Table 5.1, and the tension of the 2 position transducers) the spring
constants would be different than specified by the manufacturers. This meant that the
spring constants needed to be measured again. This calibration of the force balance is
described in Chapter 6.
5.3
Wind Tunnel Modification
To simulate the effects of forward flight, an existing low-speed wind tunnel was
used. It was desired to put the entire mechanism, which had a 38 inch wingspan, and test
assembly in an incoming flow of 5m/s. As the wind tunnel had a 30 inch by 30 inch
cross section and a minimum speed of 9 m/s, modifications were necessary. Since the
mechanism with the wings was approximately 38 inches in span, and it was desired to
avoid wall interference effects, the closed return tunnel was converted to an open-jet
closed return tunnel.
First the 30 inch by 30 inch test section was removed, allowing the air to exit into
an open room. The original tunnel consisted of a convergent section where the flow
entered a 60 inch by 30 inch cross section which then transitioned to the working cross
section. Next, this convergent section was removed, allowing for a lower tunnel velocity
and a 60 x 30 inch working section. It was also necessary to recapture the air and guide it
back into the tunnel. In order to do this, an aft-end collector with a large radius was
48
constructed. The collector was a bell-mouth shaped collar made out of 1/16 inch
plywood skin with a wooden exoskeleton. A view of the recapture collar, the test
assembly and the mechanism in the entire experimental setup can be seen in Figure 9.
An actual image of the recapture collar can be seen in Figure 5.5.
Collector
Test
Assembly
Mechanism
Figure 5.5: Actual View of Wind Tunnel After Modifications
Removing the test section of the wind tunnel, and allowing the flow to enter a
larger chamber without passing through a cross section reducing nozzle, allowed for a
slower flow as well as reduced wall interference effects. The modified tunnel was able to
achieve velocities as low as 4.25 m/s and as high as 11.65 m/s. The flow velocity was
approximately 2.5% lower near the edge of the flow.
49
CHAPTER 6: TEST EQUIPMENT CALIBRATION
One of the first tasks in any testing procedure is to calibrate the measurement
equipment. It was necessary to convert the analog voltages output by the position
transducers and encoder into distance and frequency measurements. It was also
necessary to write a data acquisition program to record the data to be later analyzed.
LabView was used to read the data acquired from the potentiometers, motor and
encoder. A NI6036E National Instruments data acquisition (DAQ) card was used to read
the voltage levels of the potentiometers as well as the encoder. To connect the devices to
the DAQ card, a terminal block was used: model number CB-68LP. The terminal block
offered straight line wire/pin connections to the DAQ card in the computer.
6.1
6.1.1
Calibration of Potentiometers
Measuring Spring Deflection: Position Transducers
Linear position transducers were purchased from Celesco Electronics to measure
spring deflection. The transducers chosen were the Compact String Pot SP1 with a 12.75
inch full stroke range. They output a voltage depending on the amount a cable is
extended. The SP1 has 0.05% full stroke repeatability and an accuracy of 0.25%. The
cable tension was 7 ounces.
One transducer was used in the vertical direction (lift) and one was used in the
horizontal direction (thrust and drag). The transducer measuring thrust and drag was
bolted to the actual testing structure, and its cable was extended and attached to the
50
mechanism itself. The transducer measuring lift was bolted to the top linear bearing
housing and the cable was again extended and attached to the mechanism. As the
mechanism moved within the assembly, output voltages were recorded, corresponding to
positions. These positions were converted to forces based on spring constants of the
springs in the force balance.
6.1.2
Wiring
The transducers output an analog voltage signal from 0-12 volts. There was a
direct linear relationship between voltage and distance the cable was pulled, meaning if
the cable of the transducer was extended 12 inches, the output voltage will be 12 volts,
given a 12 volt supply to the device. However, LabView can only accept voltage signals
from -10 volts to +10 volts. Since a 12 volt car battery was used to solely power the
transducers (an effort to isolate the signals from ambient noise), a potentiometer was
wired to the battery to regulate the voltage to +10 volts.
The ground pins of both the transducers were connected to the common ground on
the battery. The supply pins were both connected to the variable pin on standard rotary
potentiometer, allowing the voltage to be regulated at +10 volts. Using this
potentiometer maintained the voltage at the desired value as the battery drained down
below 12 volts.
6.1.3
Distance Calibration and LabView
From the signal pin of the transducer the variable voltage level was sampled. The
continuous scan function (C-Scan.vi) in LabView was used. This function took time
sampled measurements (in this case voltage measurements) of a group of channels. Since
51
there were two transducers, two channels were used. This data was stored in a circular
buffer and returned a specified number of scan measurements. The sampling rate was
5000 samples per second over a 10 second time period. Next, the data was stored in a
data array, and then the using an averaging function, the mean of the data was taken.
This was done to compensate for errors in data acquisition, and allowed for better data
samples, smoothing out inconsistent peaks. The voltage was then output to the screen.
This voltage was output predominantly for monitoring purposes ensuring the transducers
were working properly.
Next the voltage acquired through the DAQ card was converted into a distance.
There was no longer a 1:1 relationship between voltage and distance since the transducers
were receiving 10 volts instead of 12. An experiment was performed to determine the
new ratio. When the transducer was fully released (at the 0 inch position), there were 0
volts across it. However when the potentiometer was fully extended to a measured 12.75
inches, it was noted that the voltage was 9.85 volts across it. Dividing the two yielded a
ratio of volts per inch. Equation 6.1 gives an overview of how the required ratio of
volts/inch was obtained.
9.85V
V
= 0.773
12.75in
in
Equation 6.1
Using the above obtained ratio of 0.773 volts per inch, the averaged voltage output
to the screen was divided by the ratio to yield a stretch distance. The position transducers
were attached to the device in the force balance. Now as the mechanism moved, the
distance was measured and output to a LabView data panel.
52
6.2
Calibration of Force Balance
The force balance needed to be calibrated because multiple springs were now used
in each direction. In addition the mechanism when placed in the balance, compressed the
springs. This in turn yielded new spring constants which needed to be measured and put
into the data acquisition program.
In order to measure the new spring constants a typical set of experiments to
measure spring rates was carried out: weights were applied to the spring, their
displacement was measured, the data was plotted, and the spring constants were obtained
from the graph. Since the linear transducers were already connected to the mechanism,
weights could be directly attached to the mechanism. Again, the amount the mechanism
translated was output to the LabView front panel. This was how distance was measured
for the calibration experiments. This experimental data was corroborated with theoretical
values as a second check to determine the validity of the results.
6.2.1
Calibration of ±X Direction (Thrust)
First, the new spring constant was calculated theoretically. The spring constant of
the Spring 3 (from Table 5.1) was 0.25 lb/in. The position transducer was used to
balance it on the other side. The transducer consisted had a cable recoil tension of 7
ounces or 0.4375 lb/ft or 0.036 lb/in (k1 in Equation 6.2), while it was known the spring
constant of the custom made spring was 0.25 lb/in (k2 in Equation 6.2). The combined
spring constant is determined theoretically in Equation 6.2.
k eff = k1 + k 2 = 0.25 lb in + 0.036 lb in = 0.29 lb in
53
Equation 6.2
A range of weights, from 100 g to 1 kg were tied to the mechanism and hung over a
low friction pulley.
The experiments were repeated 3 times, and the values were
averaged. Table A.1 in Appendix A displays the data used for this calibration. Figure
6.1 shows the experimental setup to measure the new spring constant.
Pulley
Mechanism
Spring for
Drag/Thrust
Weight
Figure 6.1: View of Force Measurement for Drag and Thrust
When the spring calibration experiment was completed and the data plotted, it
was found that the measured spring constant was approximately 0.32 lb/in. Figure A.1 in
Appendix A shows a plot from which the spring constants were obtained. This variation
can most likely be due to the friction between the spring and the aluminum rod over
which it rests. The static friction between these two can be quite significant, especially
when very low loads such as these (less than half a pound) are being used.
6.2.2
Calibration of ±Y Direction (Lift)
To measure the spring constant in ±Y direction, weights were again attached to
the mechanism and allowed to hang down via the use of a low friction pulley. In order to
54
lift the mechanism up, and thus compress the top spring, the pulley was clamped to the
top of the testing assembly directly above the top spring. Figure 6.2 displays the
procedure for testing the spring constant of the top spring.
Pulley
Top Spring
for Lift
Linear
Transducer
Weight
Mechanism
Figure 6.2 : View of Measuring Spring Constant of Bottom Spring
The value of the spring constant was measured to be 0.60 pounds per inch. The
specified value from the manufacturer was 0.28 pounds per inch. As the top spring was
cut down in length from 12 inches to 6 inches, this yielded a theoretical increase in spring
constant of 50%, from 0.28 pounds per inch to 0.56 pounds per inch. The measured
value of 0.60 pounds per inch is very close and the 0.04 pounds per inch deviation can be
most likely explained through friction, and that the spring was cut down to approximately
6 inches. Equation 6.3 and Equation 6.4 show how the spring constant was estimated
theoretically.
55
l new
6in
=
= 0.500
l orig 12in
Equation 6.3
0.28 lb in
= 0.56 lb in
0.5 lb in
Equation 6.4
Appendix A displays all of the raw and analyzed data for this calibration
measurement.
6.3
6.3.1
Calibration of Motor and Encoder
Wiring of Motor
The motor was powered directly from a dedicated power supply. It was not
feasible to power the motor from LabView as the maximum current able to be provided
by the card was 5 mA, and the maximum voltage was 10 V. With this being a 12 volt
motor and capable of drawing up to 0.74 amperes it made more sense to use a dedicated
power supply. The motor was controlled directly from the power supply by increasing
the voltage to increase the rotational speed (and thus flapping frequency) or by lowering
the voltage to decrease the rotational speed.
6.3.2
Wiring of the Optical Encoder
As previously stated, the optical encoder hub-wheel was mounted directly to the
drive shaft, and the encoder module was mounted to the bearing mounting plate. The
encoder module consisted of 5 pins: ground, index, channel A, channel B, and supply.
56
The encoder module must be supplied with +5 volts and draws typically 57 mA of
current. A dedicated power supply was used to power the encoder module due to voltage
and current limitations of the DAQ card. This ensured that the encoder module was
supplied with as much current as necessary. The supply pin was connected to the
positive node of the power supply, while the ground was connected to the common on the
power supply. The ground on the power supply was also used as the common ground.
Channels A and B were each connected to channels AI (analog input) 2 and 3. The index
channel was connected to AI 4. The grounds for each of the AI pins were connected to
the common power supply dedicated for the encoder.
6.3.3
Encoder Calibration and LabView
The index channel output of the encoder went high once per revolution, coincident
with the low states of channels A and B, nominally ¼ of one cycle. Channel A and B
pulsed high at approximately 0.4 volts and the phase lag or lead between the channels
was approximately 90 electrical degrees.
From the pulses recorded from the encoder it was necessary to measure the angular
position as well as the speed of the shaft. Measuring angular position was a fairly
straightforward task. To do this a LabView program was written which used the inputs
of channel A, channel B and the index channel to determine position and angular speed.
This information was acquired, stored in a buffer for 5 seconds and output to a data file.
57
6.4
Data Acquisition
In order to observe the data trends over a defined period of time, in order to see
trends and instantaneous values in force and distance per flap, it was necessary to export
the data to a file. A LabView VI was written to do this. It was capable of exporting data
as either a plain text document or a spreadsheet file (Excel). The output to this file were
columns of data, with columns corresponding to thrust distance, lift distance, lift force,
lift distance, flapping frequency, flywheel position, etc.
The front screen of the VI had a “Record Data” button, which when pressed would
record “x” seconds of data, where “x” was a time in seconds preset. Generally, 5 seconds
of data were recorded. As soon as the record button was pressed, the LabView program
would start recording data as soon as the first window of the encoder wheel passed
through the LED and read “high”. All of the necessary parameters were recorded every
0.72° of the encoder wheel (the distance between encoder windows) This data was
written to an array and stored in memory until data was taken for 5 seconds. The
program then output this information to an Excel spreadsheet.
6.5
Angle of Attack Calibration
One of the main variables in generating aerodynamic forces is the angle of attack of
the wings. As previously stated in Chapter 2, the angle of attack is directly related to the
amount of forward thrust generated in flapping wing flight. Therefore in this experiment,
various angles of attack were explored. The angle of attack calibration was done using a
large protractor with a wooden backing attached to a precision machined aluminum baseblock. The block was machined to ensure it was flat with respect to the horizontal.
Figure 6.3 displays picture of what the calibration tool looked like.
58
Calibration Tool
Wing
Figure 6.3: Angle of Attack Calibration Tool
The calibration tool was placed behind the root of the wing, in front of the body
and eye calibrated to the desired angle. The tool was capable of calibrating for both
positive as well as negative angles of attack.
59
CHAPTER 7: TESTING
7.1
Testing Approach: Test Matrix
The test parameters studied for this research investigation consisted of an evolving
test matrix. An initial matrix was proposed based on literature and research. As testing
progressed, certain cases were omitted due to their lack and poor performance. Other
cases were investigated further if the mechanism produced good results. Table 7.1 shows
the final test matrix used for Wing 1.
Table 7.1: Test Matrix for Wing 1
Wind Tunnel Speed:
Angle of Attack:
Flapping Frequency
2 Hz
3 Hz
4 Hz
0°
0 m/s
7.5°
Cases
15°
0°
5 m/s
7.5°
Cases
15°
Initially, tests were to be conducted at all of the cases listed above. However,
during testing it was believed that the cases highlighted in black would not be of interest
based on neighboring results. For example, the case involving testing at 2 Hz, and at an
angle of attack of 7.5° was tested at 0 m/s as well as 5 m/s. No lift was generated
flapping at 2 Hz, and virtually no thrust was generated. Thus, it did not make sense to
flap at a frequency of 2 Hz anymore and none of the other 2 Hz test conditions were
investigated further. Originally a flow speed of 10 m/s was part of the test matrix.
However, after the first test at this flow speed it was discovered that the mechanism did
not have enough power to overcome the drag. The mechanism was pushed to the very
60
rear of the force balance resulting in 0 forces produced. No further tests were conducted
at this flow speed as it was believed no useful information would be observed.
The testing for Wing 2 was an evolving approach as well. Not all of the cases for
Wing 1 were repeated with Wing 2. Only the best cases of Wing 1, i.e. the ones that
generated the most lift and thrust, were repeated again with Wing 2. Table 7.2 below
shows the testing matrix ultimately used for Wing 2.
Table 7.2: Test Matrix for Wing 2
Wind Tunnel Speed:
Angle of Attack:
Flapping Frequency
3 Hz
4 Hz
0 m/s
0°
Cases
0°
5 m/s
7.5°
Cases
15°
In order to generate meaningful results from the experiments, a certain set of
analyses was performed on the data. First, high-speed video was taken of each case.
Using the high-speed video and the analysis software associated with it, it was possible to
graph the wing tip and the wing root as a function of time for each set of flaps. Next,
using the output from the LabView software and the resulting output encoder counts (and
thus position of the flywheel), it was possible to get the lift and thrust forces generated
versus the phase of the flap. The lift and thrust forces were then cycle averaged and
correlated with wing position obtained from the high speed camera. This would give an
idea as to how wing behavior affected the aerodynamic forces generated by the
mechanism.
61
7.2
Encoder Position, Wing Tip and Root Position Correlation
The high-speed video served three purposes. First, it served as a check that the
frequency output by the encoder was accurate. Second, when the start times and
positions of the encoder and high-speed video were synchronized, it was possible to
visually observe exactly how the wing behaved during the flapping cycle and the
associated aerodynamic forces generated by that position in the flap. Third, it made it
possible to see how the wing flexed during various points in the flapping cycle.
This correlation was done for all of the experiments performed with Wing 1. It was
not done for Wing 2 since it had already been proven 6 times with Wing 1 that the
encoder position and wing positions line up, and it was a very tedious process. The
synchronization discussed here in detail is for a single case; the process for each of the
other cases was identical. The graphs for each of the other cases can be seen in Appendix
B. The process discussed in detail is the 0 m/s, 3 Hz and 0° AoA case.
Data was recorded every 0.72° of the encoder wheel. This was the spacing
between the encoder windows. One of the columns of the data file was encoder position
in degrees, from 0 to 360. With knowledge of the flapping frequency, it was possible to
get an estimate for the time it took for the encoder wheel to turn 0.72°. This time was
correlated with the time it took for the wing to make a complete flap. For example, the 0
m/s, 3 Hz, and 0° AoA case discussed here had an actual flapping frequency of 3.292 Hz.
This meant that one flap took approximately 0.3038 seconds.
In order to correlate wing positions from the high-speed camera with position from
the encoder, it was necessary to synchronize the two. The high-speed video was
advanced frame by frame until the wing started to move, and this position was given time
62
0. As the data acquisition program started writing data as soon as the encoder moved 1
window, or 0.72°, the encoder position could be synchronized with the high speed video.
Each successive video frame was 1.667 ms apart as the video camera recorded at
600 frames per second, while the position data was collected for every 6 frames, or every
10 ms. During analysis, an earth-fixed coordinate frame was superimposed on the video,
and, every 10 ms, the position of the wing tip and root was recorded using the coordinate
system in the video analysis software.
Figure 7.1 shows the encoder signal plotted with the wing displacement of both the
root and the tip for 5 flapping cycles. Based on the encoder frequency, each flap took
approximately 0.304 seconds ±5 ms. Using the high-speed camera, the average period of
the wing’s root is approximately 0.308 seconds ±1.6 ms. This data indicates that the
force data synced to the encoder and the wing positions can be aligned.
The same analysis performed on other cases produced similar results. From Figure
7.1 it can be seen that the wing root is displaced further on the upstroke than on the
downstroke which is due to the mechanical bias in the design as discussed in Chapter 4.
From the graph, it can be seen that the encoder position lines up very closely with
the wing root position. The period of the wing root was an average of approximately
0.308 ms, with the wing tip having an average period of 0.310 ms. The period as
established from the encoder is approximately 0.304 seconds. This analysis was done for
all of the cases in the test matrix. The time for each flap of the tip and the root matched
the period of the encoder wheel very closely. This proves that the high-speed video
camera and the encoder position were properly synchronized.
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Figure 7.1: Encoder Position, Wing Root & Tip Displacements vs. Time
7.3
Filtering of Force Balance Inertial Effects
An effort was made to separate the inertial forces from the aerodynamic forces
present in the force balance as the mechanism flapped its wings. This was done by
attaching aluminum rods in the place of each of the wings. These aluminum rods were
chosen such that they had the same mass distribution and center of gravity as each of the
wings. These rods were then flapped and the data recorded using the data acquisition
software as previously described. The inertial motions of the mechanism caused it to
move in both ±X and ±Y directions. These motions were recorded for each of the cases
and subtracted from the data acquired when the mechanism was flapped with the actual
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wings to yield pure aerodynamic forces. Figure 7.2 shows an image of the aluminum
rods with attached masses connected to the mechanism’s main flapping shafts.
Figure 7.2: Setup for Spring Dynamics Correction
The mechanism was then flapped at 2, 3, and 4 Hz for both Wing 1 and Wing 2.
The data acquisition program was run and same data was recorded as if the mechanism
had regular wings attached. The resulting data file consisted of inertial vibrations of the
mechanism in the thrust and lift directions. This data was collected for each of the cases
investigated by the test matrix and subtracted from the resulting data for the respective
test condition.
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7.4
Aerodynamic Forces Generated Without Flapping
In order to determine if it was actually beneficial for the mechanism to flap its
wings, it was necessary to benchmark the test cases against a no-flap condition. This
would give an estimate as to what kind of lift, thrust or drag would be generated by the
mechanism when it was not flapping its wings. To do this, the data acquisition program
was initialized and set to record for approximately 13 seconds. This experiment was
performed on Wing 1. It was not performed on Wing 2 because both wings had exactly
the same surface area exposed to the incoming flow.
First, the mechanism was oriented with the wings at 0, 7.5 or 15°.
Next, the data
acquisition program was set to run for 13 seconds. Third, the wind tunnel was turned on,
where the speed increased to 5 meters per second. It took the wind tunnel approximately
5 to 6 seconds to stabilize at 5 meters per second. After 13 seconds, the data acquisition
program wrote all of the data stored in its memory to an Excel spreadsheet.
It should be noted that there was a tendency for the wings to return to 0° when the
airflow was turned on. This was due to the clearances in the mechanism which caused
the pitching motions. With the flow on, the 0° offset remained at 0°. The 7.5° offset
stabilized at approximately 2°, while the 15° offset stabilized at 5°.
From Figure 7.3, it can be seen that drag varied with angle of attack as expected,
with higher angles of attack producing higher drag. This was due to increased wing
surface area exposed normal to the flow at higher angles which increases drag.
Overcoming its drag was one of the criteria for the mechanism designed in this thesis to
be “successful”.
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To measure lift, a similar approach was taken. Again the data acquisition system
was set to record for 13 seconds, and then the tunnel was turned on until the wind speed
stabilized at 5 meters per second. However, after the first lift test it was found that the lift
force was not large enough to overcome the static friction in the linear bearings on which
the mechanism rode. To counter this problem, the mechanism was tapped with a finger
during the test. Once tapped, the mechanism would overcome the static friction and
stabilize at a different value. This finger tapping was done 4 times and the resulting lift
values were averaged. Figure 7.3 below shows the effects of tapping the mechanism to
overcome static friction and obtain accurate readings of lift.
Figure 7.3: Lift & Drag Force vs. Time @ 5 m/s Without Flapping
To counter the effects of the mechanism’s clearances causing the wings to deviate
from their set initial angles of attack, a small piece of aluminum was wedged in place.
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The wings were then pinned at -7.5°, 0°, 7.5° and 15° angles of attack and the lift was
measured in 5 m/s incoming flow. Figure 7.4 displays the results. The average lift
values from when the wings were not pinned and deviated from their initial set angles of
attack are also plotted in Figure 7.4. Unsurprisingly, it was found that a negative angle of
attack produced negative lift. At -7.5° -0.016 lbs of lift were generated. The lift then
steadily increased to 0.032 lbs when the angle of attack was 7.5°. At 15° positive lift was
generated as well (0.02lbs), but slightly less than at 7.5°. This decline in lift can be
attributed to flow separation at the trailing edge of the wing.
Figure 7.4: Lift vs. Angle of Attack @ 5 m/s Without Flapping
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CHAPTER 8: ANALYSIS OF RESULTS
8.1
Wing 1 Phase Lag
One of the most noticeable effects of having a flexible wing was that the wing
flexed such that the wingtip generally lagged the wing root. Video evidence of this phase
lag can be seen in Figure 8.1 and Figure 8.2 below. These images are from the 0 m/s, 3
Hz, and 0° angle of attack case. The images taken in Figure 8.1 and Figure 8.2 are stills
captured from the high-speed video camera. Note the obvious phase lag on the upstroke
in Figure 8.1 where the root of the wing is already well on its way in the upward motion,
while the tip has just started the upstroke. Figure 8.2 shows a similar result for the
downstroke, where the root is already into the downstroke while the tip is just beginning
to travel downward.
Figure 8.1: High Speed Video Still Image of Wing 1 Beginning Upstroke
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Figure 8.2: High Speed Video Still Image of Wing 1 on Downstroke
Figure 8.3 below shows the wing root and tip positions with theoretical curves fit
to each for the Wing 1 case tested at 0m/s, 3 Hz, and 0° AoA. The curves were fit using a
sinusoidal function of the form:
f (t ) = A ⋅ sin(ω (t + ∆t )) + B
Equation 8.1
In Equation 8.1, t is time, ω is frequency in radians, A is the amplitude of the
flapping motion, ∆t is the phase shift, and B is the offset of the curve used to account for
the bias in the mechanism. It was found that the experimental data was closely
approximated by the sinusoidal functions, however there were some differences. From
the curve fits, it was found that the difference in phase between the wing root and the
wing tip was 3° on average.
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Figure 8.3: Wing 1 Root & Tip Displacement with Curve Fits
Phase lag was calculated for 2 discrete points: when the wing when the wing was
at the end of the downstroke, and also when the wing was in the center of the flap on the
upstroke. The center of the flap on the upstroke was chosen because at this point the
wing had its highest velocity, for both the tip and the root. Equation 8.2 was used to
calculate the phase lag at the end of the downstroke, while Equation 8.3 was used to
calculate the phase lag at the center of the upstroke.
tTip − t Root
t1Flap
⋅ 360 °
Equation 8.2
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t 0,Tip − t 0, Root
t1Flap
⋅ 360 °
Equation 8.3
In Equation 8.2, tTip is the time the wingtip is at its minimum position. TRoot is the
time the root is at its minimum position, and t1 Flap is the time the mechanism takes to
complete one complete flap. In Equation 8.3, t0, Tip is the time the wingtip is at its
minimum position. T0, Root is the time the root is at its minimum position, and again t1 Flap
is the time the mechanism takes to complete one complete flap. From the above
equations, it was found that when Wing 1 was changing direction from the downstroke to
the upstroke, the wingtip lagged the root by an average of 35.5°. However, when the root
was well on its way on the upstroke, the tip trailed by as much as an average of 58°,
roughly corresponding to the position depicted in Figure 8.1.
Upon further examination of Figure 8.1, it can be seen that the wing has buckled in
between the second and third structural members. Over time this has obvious negative
effects as the wing will most likely fail due to fatigue. However it is not clear if the wing
buckling has adverse effects on the generation of aerodynamic forces. Examining Figure
8.3, it can be seen the buckling phenomenon repeats. Kinks in the wing tip position on
the upstroke occur at regular intervals such as at times of 800 ms, 1125 ms, and 1450 ms.
This wing buckling is also apparent in the lift, but is not significant. This is most likely
due to the adaptive nature of the wing’s membrane which can react to situations such as
these. A parallel can be drawn between buckling behavior and such effects as
encountering a gust or hitting a stationary object which may cause wing buckling. The
wings ability to correct for these phenomena without having a significant effect on the
generation of thrust and lift is one of the major benefits of having flexible wings.
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A third effect of having a flexible wing is also apparent in Figure 8.3 where the
velocity of the wing tip can be seen to vary with time. The wing tip velocity is greater
near the end of the downstroke relative to the beginning of the downstroke as evidenced
by the greater vertical spacing between the points which were taken at constant time
increments. Similar behavior is seen on the upstroke where the tip speed is greater near
the end of the upstroke. This behavior was related to phase lag, where the wing tip
lagged the root as it traversed the flap. On the downstroke, the maximum wing tip
velocity was reached just after the wing passed the midpoint of the downstroke. At this
point the velocity was found to be approximately 5.67 m/s. A slightly higher velocity of
5.8 m/s was measured on the upstroke at the wing tip. This increase in speed of the wing
due to flexibility should result in higher forces on the wing, and is discussed in Section
8.4.4 and Section 8.5.2.
8.2
Wing 2 Phase Lag
Figure 8.4 and Figure 8.5 below show the resultant phase lag of Wing 2 during the
flapping cycle of the 5 m/s, 4 Hz, 7.5° AoA case. From Figure 8.4, it can be seen that the
wing tip is well on its way on the upstroke as the wing tip is flexing in an effort to slow
down and compensate for the change in direction. Figure 8.5 shows the phase lag as the
wing is beginning the downstroke. As was the case with Wing 1, the phase lag on the
upstroke is more dominant than that of the downstroke. This was due to the nature of the
wing fabrication process; the wing was not equally pliable in both directions. Even based
on the just the images from the high speed video camera, it is visually obvious that the
phase lag is much smaller than that of Wing 1.
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Figure 8.4: High Speed Video Still Image of Wing 2 Beginning Upstroke
Figure 8.5: High Speed Video Still Image of Wing 2 Beginning Downstroke
Figure 8.6 shows a plot of the wing root and tip displacement as a function of time
with theoretical curves fit to the data using Equation 8.1. When performing the high
speed video analysis on Wing 2, the data was only recorded out to 2 flaps excluding the
startup transients. Phase lag for Wing 2 was calculated the same way as for Wing 1 using
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Equation 8.2 and Equation 8.3 as described in Section 8.1. From Figure 8.6 below it
appears that the curve fit for the tip does not match the experimental data very well. The
largest variation appears to be on the downstroke, while the curves appear to match the
data for the upstroke quite well. This is most likely due to the fact the leading edge of
Wing 2 is very stiff until the very tip, approximately 2 to 3 inches inboard from the tip.
Figure 8.6: Wing 2 Root & Tip Displacement with Curve Fits
As was the case with Wing 1, it was found that most of the phase lag for Wing 2
occurred as the wing changed direction from the downstroke to the upstroke. The phase
lag at this point was calculated to be an average of approximately 27.7°, roughly
corresponding to the image shown in Figure 8.4. This is much smaller than the value of
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35.5° with Wing 1. The phase lag when the wing was at the center of its upstroke was
found to be an average of 23.5°, which is much smaller than the value of 58° for Wing 1.
It should be noted that Wing 1 had greater phase lag when it was at the center of the
upstroke than when it was at the end of the downstroke. However, Wing 2 had greater
phase lag at the end of the downstroke. The reason for this is most likely because Wing 1
was overly flexible due to buckling. The lag between Wing 1 and Wing 2 only changed
by approximately 7.9° during the center of the flap, but by 34.5° at the bottom of the flap.
These differences suggest that it is almost inevitable that phase lag will occur during the
center of the upstroke, as the tip will always be trailing the root by some angle unless the
wing is perfectly rigid. However, the incorporation of a stiffer wing can at least help
reduce the phase lag at the point where the downstroke ends and the upstroke begins.
8.3
Wing Pitching Motions
Figure 8.7 shows the pitching motions of Wing 1 and Wing 2 as they complete
one flap. These pitching motions were obtained from the data acquired from the highspeed video camera. As Wing 1 starts its flap, at the 0° position, it has a positive angle of
attack. As it continues through the first 30° of the flap cycle, the angle of attack (relative
to the earth) decreases approximately 15°. At this point the angle of attack was constant
and slightly negative. This is the case throughout the majority of the downstroke and
starts to increase again at approximately 180° and levels off for the upstroke at about
240°. These pitching motions are similar to those produced in other flapping wing
mechanisms.
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Figure 8.7: Wing 1 Pitching Motions Produced During Flapping
From the graph it can be seen that the pitch envelope for both wings did not
noticeably change. There is still a about a 15° variance in which the wing moved from its
set position. The main difference between the two wings is that Wing 2 changed pitch at
a faster rate than Wing 1. The main reason for this was due to increased stiffness. The
increased stiffness does not lend itself to as much damping and phase lag in the flapping
motion, and as a result is able to change directions quicker.
The main reason for this variability in pitch were clearances in the connection
between the main flapping shafts and the crankshafts where the shafts were pinned
together. From the plot, the variability is approximately 15°. There was also some
change in pitch due to the flexible nature of the wings, but was almost negligible when
77
compared to the cause of pitch from the mechanism. It is unlikely that the pitching
envelope will increase or decrease due to increasing airspeed or flapping frequency. This
is because the maximum and minimum angles are governed by the amount of clearance
between the main flapping shafts and the pin used to hold them together. As the initial
angle of attack of the mechanism is altered, the peaks will differ. This essentially
introduces a bias in the pitch envelope changing the maximum and minimum points.
However it should be noted that as the mechanism continues to flap over an extended
period of time, the envelope will likely increase due to wear between the connections.
8.4
8.4.1
Analysis of 1st Generation Wing
Results: Lift and Thrust Force vs. Time
After all of the experiments in the test matrix described in Section 7.1 were
completed, the data was analyzed. To observe trends, the lift and thrust forces were
plotted versus time. Figure 8.8 below shows lift and thrust force versus time for the 0
m/s, 3 Hz, and 0° AoA case. This data is graphed out until approximately 4.5 seconds.
This analysis was done for each of the other cases in the test matrix, but is not shown
because the data repeatedly followed the pattern shown in Figure 8.8. It should be noted
that a startup transient is visible in both thrust and lift generation up to approximately 550
ms.
78
Figure 8.8: Lift & Thrust vs. Time @ 0 m/s, 3 Hz, & 0° AoA
From Figure 8.8, it can be seen that the forces for both thrust as well as lift are
periodic. The lift force has a minimum at approximately -0.028 lbs and peaks at about
0.041 lbs (average). This means that the mechanism is able to generate positive lift on a
cycle averaged basis. The thrust measurements show that the mechanism produces
positive thrust throughout the flapping cycle, and consistently for the duration of the test.
The slight periodic nature of the thrust is due to the inertial effects of the
mechanism. In the graph above, the inertial effects have not been removed. When
flapping the rods as described in Section 7.3, some inertial effects were present in the
thrust direction. This is because the clearances in the mechanism and the swivel bearings
used did not purely constrain the flapping in the vertical direction.
79
8.4.2
Results: Lift and Thrust Force vs. Wing Position (Phase)
In order to cycle average the forces a Matlab program was written. First the
inertial effects in both the lift and thrust directions were subtracted from the data. Next,
the first two complete flaps were ignored as they could be misleading due to startup
transients. The data was then cycle averaged over 10 flaps from 0° to 360°. It was
known that the mechanism flapped from 0° to 360° 10 times. All of the lift forces at the
0° position were averaged, as were the thrust forces. This was done for 0.72°, or the next
turn of the encoder wheel. The same process was followed for each of the successive
recorded degrees, and the resulting data was plotted. Figure 8.9 is a cycle averaged plot
of the 0 m/s, 3 Hz, and 0° AoA case. Plots of the remaining cases in the test matrix can
be seen in Appendix B.
Figure 8.9: Lift & Thrust vs. Phase @ 0 m/s, 3 Hz, & 0° AoA
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With the information in Figure 8.9 it is possible to get an understanding of wing
position and the resulting aerodynamic forces resulting at each point in the stroke. The
start position of 0° refers to the wing root being at a maximum height position: at the very
start of the downstroke.
From Figure 8.9 it can been seen that the shape of the thrust and lift curves are
different. This is not only true for 0 m/s, 3 Hz, 0° case, but for all of the other cases as
well (see Appendix B). The generation of lift appears to be periodic in nature. As the
wing flaps downward from its initial starting position, the generation of lift begins to
increase. Somewhere during the downstroke, the lift peaks and as the end of the
downstroke approaches and the lift force begins to decrease. During the upstroke
negative lift is generated. This cycle continues as the mechanism flaps. This appears to
be as expected, with results following similar trends based on experiments performed by
others.
Thrust generation is slightly different, as the flapping wing mechanism appears to
constantly produce thrust. The reason for this is that the wing is changing its shape and
angle of attack dynamically. On the downstroke the wing is pitched down, forcing air in
the –Y direction, while in the upstroke the wing sweeps forward and up, minimizing the
movement of air in the direction causing negative thrust. For all cases the thrust is
relatively constant throughout the cycle. The magnitude of the thrust appears to slightly
increase for the higher frequency, forward flight case. Note that in all cases, the net
thrust is overcoming the natural drag of the mechanism as shown in Figure 7.3.
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8.4.3
Lift and Thrust Data to High Speed Video Correlation
Lift and thrust forces were graphed versus wing position (or phase) in Section
8.4.2. The graphs in that section gave a numerical indication of wing position and the
kinds of lift and thrust forces generated at those positions. However, it was useful to see
what the actual wing position was and how its orientation in phase affected the generation
of aerodynamic forces. This analysis was done for the 4 most interesting cases in the test
matrix. These cases and the associated wing positions can be seen in plots from Figure
8.10 to Figure 8.13.
In order to do this, still images were captured from the high speed video taken for
each case. Correlating the wing position from the video camera with the position from
the encoder was done by time as previously discussed in Section 7.2. A particular wing
position (in encoder degrees) corresponded to a time interval calculated based on the
frequency of the flap. This time from the encoder data was cross referenced with the
time on the high speed video camera. Since the times were lined up from the start of the
flapping, it was straightforward to obtain wing position screenshots from the high speed
camera. For example, in Figure 8.10, the time associated with an encoder angle of 125°
was 537 ms. In the high speed video, a time of 537 ms, corresponded to frame number
1594. The high speed video was then paused at frame 1594 and a screenshot of this
image was taken. This was the process followed for each of the 5 wing positions shown
on the graphs below. Figure 8.10 through Figure 8.13 show the high speed video
captures of Wing 1 correlated to the cycle averaged force. This analysis was done for the
4 cases which produced the most lift and thrust in the test matrix.
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In all of the 4 cases it was found that positive lift occurred on the downstroke,
while thrust was always being generated. For all 4 graphs the 0° location is where the
wing root is at its maximum height. At this point the wing is starting its downward
motion, resulting in the generation of positive lift.
Case 1 was when the mechanism flapped at 0 m/s, 3 Hz, 0° AoA, and the results
can be seen in Figure 8.10. As the wing continued to flap downwards, the lift force
increased until it reached a peak at approximately 140° and the lift force at this point was
approximately 0.036 lbs. After this, the generation of lift started to decrease and reached
a minimum at about 275°, but the force become negative when the wing was at about
250°. A minimum in lift was reached when the mechanism was on its upstroke. The
cycle then continued to repeat itself. Note that the peak positive lift is greater than the
peak negative lift and that the duration of positive lift is greater than that of the negative
lift, thus indicating that net lift is generated. The average lift generated was
approximately 0.009 lbs, while the average net thrust generated was 0.010 lbs.
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Figure 8.10: Wing 1 Position, Force & Phase Correlation @ 0 m/s, 3 Hz, & 0° AoA
Case 2 shown in Figure 8.11 includes forward flight where the mechanism is
flapped at 5 m/s, 3 Hz, 7.5° AoA. The lift curve looks slightly different than a no flow
and 0° AoA condition. Again the wing started at a maximum height position at 0°. Up to
about 100°, the lift increased almost linearly, and past this point there was a sharp
increase in the rate at which the lift force was generated. The wing reached its first
positive peak in lift force of 0.038 lbs at 156°. At this point the wing was just slightly
past being horizontal to the ground. A second lower positive peak of 0.031 lbs was
reached at 200°, at which point the wing’s root was very close to its minimum position,
while the phase lag caused the tip to trail the root when it approached its minimum
position and this continued to generate lift. It took up to approximately 180° to 220° to
complete the downstroke. This was due to clearances in the mechanism where although
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the flywheel would turn between 180° and 220°, it would not cause any force on the
flapping shafts. The location of the spacing which caused this was at the connection
point where the titanium connecting pin was attached to the main flapping shafts.
After this point the lift force begins to decrease significantly as the wing was well
on its way on the upstroke. At approximately 275° a minimum is reached on lift
generation. Although the peak lift produced was essentially the same between the first
two cases, the duration of the positive lift was greater. This is attributed to the inclusion
of the incoming flow. The average lift generated during this cycle was 0.004 lbs, while
the average thrust generated was 0.051 lbs. The peak lift and thrust generated here are
greater than in Case 1.
Recall the no flapping condition when the mechanism was put in a 5 m/s flow at a
7.5° angle of attack where the average lift generated was approximately 0.031 lbs. The
peak lift generated when flapping at the 5 m/s, 3 Hz, 7.5° is approximately 0.038 lbs.
The mechanism naturally produces 0.08 lbs of parasitic drag when not flapping (Figure
7.3). The average thrust force produced by the mechanism while flapping was
approximately 0.051 lbs for the 5 m/s, 3 Hz, 7.5 AoA case. This means that the
mechanism was able to produce enough force to overcome its own drag and generate
sustained net thrust. This increase in peak lift and average thrust shows that there is some
benefit to flapping.
85
Figure 8.11: Wing 1 Position, Force & Phase Correlation @ 5 m/s, 3 Hz, & 7.5° AoA
Case 3 shown in Figure 8.12 is the 5 m/s, 4 Hz, 7.5° AoA condition. The wing
again started at a maximum height position at 0°. It reached its first peak of 0.043 lbs
when the wing was at about 80°, which is 60° earlier than in the no-flow case, and
reached its second higher peak of 0.52 lbs at about 200°. Compared to the 5 m/s, 3 Hz,
0° AoA case and the 5 m/s, 3 Hz, 7.5° AoA, the duration of the positive lift greatly
increased as well as the magnitude of the force. After this point the lift decreased from
210° to about 275°, when it reached its minimum which was lower in magnitude than for
the 0 m/s case. The presence of the external flow and the increase in flapping frequency
altered the performance of the flexible flapping wing. The duration of the positive lift
was again increased as seen in the 5 m/s, 3 Hz, 7.5° AoA case. This suggests that the
increased flow was a factor in increasing the duration lift.
86
Figure 8.12: Wing 1 Position, Force & Phase Correlation @ 5 m/s, 4 Hz, & 7.5° AoA
The average lift generated during this flapping cycle was 0.043 lbs and the
average thrust generated was 0.017 lbs. Compared to Case 1, Case 3 generated more
peak and average lift as well as higher average thrust. The main reason the lift was
greater was because the flapping frequency was increased to 4 Hz and there was an
incoming air flow of 5 m/s. The increase in thrust force was due to the increase in angle
of attack from 0° to 7.5°
The last case studied with Wing 1 in detail was Case 4: 5 m/s, 4 Hz, 15° AoA.
Starting from the 0° position, the lift increased until it reached a peak value of 0.036 lbs
at about 150°. Between approximately 200° to 300° lift generation decreased, with a
minimum occurring at about 310° when the wing was well on its way on the upstroke.
The minimum in lift was much lower than the other three cases, while the peak lift was
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approximately 0.036 lbs. This maximum in lift was approximately the same as the 0 m/s
3 Hz, 0° AoA and the 5 m/s, 3 Hz, 7.5° AoA cases. The average lift generated was 0.001
lbs, while the average net thrust generated was approximately -0.007 lbs.
Figure 8.13: Wing 1 Position, Force & Phase Correlation @ 5 m/s, 4 Hz, & 7.5° AoA
This suggests that flapping frequency has limited the generation of lift in the first
two cases, while angle of attack was the limiting cause in the 4th case. In order to
ascertain whether this was indeed the case, a simple experiment was conducted. Short 2
inch strings were taped to the wing and the mechanism was flapped at 5 m/s, 4 Hz, and
15° AoA. High speed video was recorded of the flap. Figure 8.14 shows a still from the
flap. A 15° angle of attack was too high and the wing was stalling due to very high
turbulence.
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Figure 8.14: High Speed Video Showing Stall @ 5 m/s, 4 Hz, 15° AoA
From Figure 8.14 it can be seen that on the downstroke there was turbulent flow
present which caused flow separation. The pieces of the string on the leading edge stayed
in a very orderly arranged pattern, while more than half of the pieces on the trailing edge
were crooked and sideways. This indicated stall and separation of the laminar boundary
layer.
8.4.4
Wing 1 Velocity Analysis
The role of wing flexibility was estimated on the wing relative velocity. It was
found that the increase in relative velocity was enhanced by the flexible nature of the
wing. The highest velocities were found during the wing’s downstroke flap. This
analysis was based from the high speed video camera. During the flap, the highest point
of the root velocity was found and measured. Next, a specific location was chosen on the
wing approximately 12 inches outboard from the root. This point was taken as the center
89
of pressure of the wing. The point in the flap when this location traveled the fastest was
found and the velocity was measured. The same was done to obtain the maximum
velocity of the wing tip.
The highest velocity of the wing root for the 0 m/s, 3 Hz, 0° AoA case, was found
to be 0.5 m/s, and occurred as the wing root approached 150°. Assuming a rigid wing,
the velocity at the ¾ span point (12 inches outboard from the root) would have been
approximately 3 m/s. However, the wing velocity for the flexible wing was 3.5 m/s at the
¾ span point. For the wing tip, a rigid wing would have a velocity of 4 m/s where the
velocity at the tip of the flexible wing was found to be 5.67 m/s. Since the force
produced by the wing is proportional to the square of the velocity, the flexible wings
should produce more lift than their rigid counterparts. If the ¾ span point is taken as the
center of pressure of the wing, then 36% more force should be produced. It should also
be noted that this peak velocity portion of the cycle is very near that of the peak lift
shown in Figure 8.10.
For Case 2 at 5 m/s, 3 hz, and 7.5° AoA, the peak speed of the wing root was found
to be 0.54 m/s. This was at approximately 150° corresponding with the 156° location in
the flap of the first peak of maximum lift. Assuming the wing was rigid, a point at the ¾
span point would be about 3.24 m/s, while the velocity at the wingtip (16 inches outboard
from the root) would be approximately 4.32 m/s. The wing velocity of the flexible wing
at the ¾ span point was found to be 3.71 m/s, while the speed of the wingtip was
measured at 5.8 m/s. With the addition of the incoming flow of 5 m/s at the ¾ span
point, the flexible wing has a relative wind of approximately 6.22 m/s versus 4.9 m/s for
the rigid wing. This shows again that the flexible wing should perform better than its
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rigid counterpart. The addition of the incoming flow as well as the angle of attack
appears to increase the wing velocities as well. A possible reason for this increase in
velocity due to a higher angle of attack is because the surface area normal to the flapping
direction was reduced. Having a 0° AoA should cause the highest positive and negative
lift force since the wing has the most surface area exposed normal to the direction of flap
and since drag is directionally proportional to the surface area. Increasing the angle of
attack reduced the surface area normal to the direction of the flap and thus decreased the
drag force, thereby increasing the velocity.
For the third case of 5 m/s, 4 Hz, 7.5° AoA, the peak speed of the wing root was
found to be 0.635 m/s. Again, assuming a rigid wing, the velocity at the ¾ span location
was 3.81 m/s. The velocity for the flexible wing at a point 12 inches outboard was found
to be 4.5 m/s. With an incoming flow of 5 m/s, the relative wind was 6.73 m/s for the
flexible wing versus 6.29 m/s for the theoretical rigid wing. Thus the flexible wing
would be expected to produce on the order of 15% more lift than its rigid counterpart.
Note that the advantage gained by the flexible wing has decreased as the forward velocity
increases. Further, the advantage of flapping is also decreased with forward speed.
However, the forward velocity is not the only factor as seen in the 2nd and 3rd cases,
where velocity increased only marginally; therefore, relative angle of attack was an
important factor as well.
The fourth case was the 5 m/s, 4 Hz, and 15° AoA case. The velocity of the wing’s
root was measured to be approximately 0.621 m/s at the peak point. Taking a rigid wing
and extrapolating the velocity at the ¾ span would be approximately 3.7 m/s while the
velocity at the tip would be approximately 5 m/s. The flexible wing showed that it
91
moved air with a velocity of approximately 4.3 m/s at the ¾ span point. With the
incoming flow of 5 m/s, the increase in air velocity for the flexible wing at this point was
6.6 m/s and 6.2 m/s for the rigid wing.
Although the data might seem to indicate that an increase in wing flexibility leads
to an increase in lift, there must be some reasonable limit for the amount of flexibility the
wing has. This was concluded after looking at the high speed camera as well as
observing the forces generated by Wing 1. The buckling phenomenon as previously
described caused the wing to lose structural stability. This in turn caused the wing to
produce less lift and thrust. A second negative effect was the phase lag apparent in Wing
1. The wing tip trailed the root by as much as 60°, another factor which most likely
reduced lift and thrust forces.
8.5
8.5.1
Analysis of 2nd Generation Wings
Lift and Thrust Data to High Speed Video Correlation
The same method of correlating wing positions from the high speed camera to the
encoder positions on the drive shaft was carried out and this correlation can be seen in
Figure 8.15 through Figure 8.21. From these graphs, it can be seen that Wing 2 had
maximum and minimum peaks in lift at similar points to Wing 1. The thrust generation
is similar as well in that it is constant.
For Case 1, 0 m/s, 3 Hz, 0° AoA shown in Figure 8.15, it can be seen that the lift
force started to increase steadily until it reached a maximum at approximately 130°. The
maximum lift generated during this cycle was 0.08 lbs. The peak was slightly earlier
than that of Wing 1, and approximately twice as much positive lift was generated. At this
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point, the wing was just past the horizontal point with respect to the ground. As the wing
finished the downstroke and continued through the upstroke, the lift started to steadily
drop and reached a minimum peak at 310°. This was the fastest point on the upstroke,
and thus makes sense that a minimum was seen at this location in the flap. The average
lift produced was 0.019 lbs, while the average thrust generated was 0.032 lbs. In
contrast, Wing 1 produced 0.01 lbs of average lift and 0.01 lbs of average thrust.
Comparing this flapping condition between Wing 1 and Wing 2, the impact of wing
flexibility can be seen. Wing 2 stayed quite rigid compared to Wing 1 during the flap and
exhibited no buckling.
Figure 8.15: Wing 2 Position, Force & Phase Correlation @ 0 m/s, 3 Hz, & 0° AoA
The flapping condition of Case 2 (5 m/s, 3 Hz, 7.5° AoA) incorporated the
inclusion of forward flight. The results were similar to those of Wing 1. From the 0°
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initial point, where the wing was just starting the downstroke, the lift force started to
increase, and reached its first peak of 0.199 lbs at approximately 135°. There was a
second maximum peak which occurred at approximately 220° where the value of
instantaneous lift was 0.15 lbs. From this point the lift decreased at a much higher rate
and become negative when it was in the middle of its upstroke at about 270°. Wing 2
reached its maximum before Wing 1 and the resulting peak lift was much higher. The
two maximums of Wing 2 were spread over 80°. This increase in lift duration was most
likely due to the incoming air flow. The average lift generated during this flapping cycle
was 0.075, while the average thrust produced was 0.051 lbs. Flapping Wing 1 at this
same condition produced 0.004 lbs of average lift and 0.053 lbs of average thrust. There
was a significant improvement changing to Wing 2 in increasing the average lift; as the
lift was increased by an order magnitude. There was very little change in thrust
generated however. The reason for this was that there was some difference in wing
positions between Wing 1 and Wing 2 during the flapping cycle, and this can be seen in
Figure 8.16 and Figure 8.11. This was specifically evident at 120° and 310° in the flap.
At the 120° point the flexible wing has a higher angle of attack on the downstroke than
the less flexible wing. At the 310° point Wing 1 exhibited large buckling deformation
while Wing 2 had a higher angle of attack on the upstroke. This was a direct effect of
increasing the wing stiffness.
94
Figure 8.16: Wing 2 Position, Force & Phase Correlation @ 5 m/s, 3 Hz, & 7.5° AoA
Case 3 is the 5 m/s, 4 Hz, 7.5° AoA condition (Figure 8.19). This case was
similar to that of Wing 1 in that there were 2 peaks of maximum lift. Unlike Wing 1, the
lift produced by Wing 2 reached a maximum of 0.293 lbs at approximately 140° very
sharply. At approximately 220° the lift force dropped quite steeply to a lesser peak of
0.165 lbs, unlike Wing 1 whose lift curve was more spread out. At 300° the wing started
to produce negative lift, and this point it was well on its way on the upstroke. This was
the best lift case where the mechanism produces almost 0.3 lbs of lift. This was also the
best thrust condition where the mechanism produces 0.06 lbs of net thrust. At the 100°
position it can be seen that the wing is quite flat on the downstroke, meaning it was more
parallel to the flapping motion than Wing 1 at the same condition. This meant that it was
able to move more air and produce more lift force. On the upstroke at 300° Wing 2 had a
95
very steep angle of attack; this minimized down force and increased net lift produced.
The average lift produced was 0.143 lbs, while the average thrust produced was
approximately 0.067 lbs. By contrast, Wing 1 at the same flapping condition produced
0.043 lbs of average lift and 0.067 lbs of average thrust.
The relative angle of attack of the flexible wing was a function of the span.
Taking a point 4 inches outboard from the root of the wing, it was found that both Wing 1
and Wing 2 had an angle of attack of 4° relative to the horizontal at approximately the
100° position point in the flapping phase. Incorporating the velocity analysis for Wing 1
(Section 8.4.4) and for Wing2 (Section 8.5.2) Figure 8.17 shows the relative angles of
attack of both wings at a point 4 inches outboard from the root of the wing. 4 inches was
chosen because it was believed that this was a point where both wing would be relatively
rigid compared to each other, since the stiffest sections of both wings were closest to the
tip.
Wing 1
v = 1.25 m/s
(velocity 4 in
outboard
from)
root)
14°
U = 5 m/s
Wing 2
v = 1.10 m/s
(velocity 4 in
outboard from)
12.5°
U = 5 m/s
Figure 8.17: Relative AoAs for Wing1 and Wing 2, 4 inches Outboard from Root
From the velocity analysis, it was found that the Wing 1 had a 14° wind (or
relative velocity), while the wind for Wing 2 was 12°. Subtracting off the angle of attack
96
of both wings at the 100° point in the flap, it was found that the resultant relative angle of
attack for Wing 1 was 10° and for Wing 2 was 8°. This confirmed that the area closest to
the root was indeed stiffer for Wing 2 over Wing 1.
Figure 8.18 below shows the velocity analysis performed for both wings at the ¾
span point, at approximately 100° in the flap. This was again done using the velocity
analysis for Wing 1 from Section 8.4.4 and for Wing 2 from Section 8.5.2. For Wing 1 it
was found that the wind from the velocity analysis was approximately 53.4°, while for
Wing 2 it was 52.3°. The relative velocity of the wing at the 100° point in the flap at a
position 12 outboard from the root of the wing was found to be 9° for Wing 1 and 5° for
Wing 2. This showed that the stiffer Wing 2 twisted less during the flap than the more
flexible Wing 1. After subtracting off the angles of attack of both wings at the 100°
position in the flap, it was found that Wing 1 had a resultant relative angle of attack of
44° and Wing 2 for Wing 2 it was 47°.
97
Wing 1
v = 6.73 m/s
(velocity at ¾
span point)
53.4°
U = 5 m/s
Wing 2
v = 6.47 m/s
(velocity at ¾
span point)
52.3°
U = 5 m/s
Figure 8.18: Relative AoAs for Wing 1 and Wing 2, at the ¾ Span Point
The reason Wing 2 had a higher relative angle of attack than Wing 1 was because
of the adaptive shaping phenomenon property inherent in all flexible membrane
structures. With the incoming free stream velocity, the trailing edge of Wing 1 was able
to twist and thus adapt to the incoming air more than the stiffer wing. This caused the
relative angle of attack to be less than Wing 2.
The 5 m/s, 4 Hz, 7.5° AoA was the case where the most lift was generated for
both sets of wings. However Wing 2 generated much more average and peak lift than did
Wing 1. The reason for this is most likely due to the fact that angle of attack was a
function of the span for both wings. Wing 1 started at a 4° angle of attack and the
relative angle of attack increased to 44°. Wing 2 also started at a 4° angle of attack, but
the relative angle of attack increased to 47 degrees. It is possible that the increase in
relative angle of attack for Wing 2 occurred further outboard from the root that it did for
98
Wing 1. This would result in Wing 2 being stiffer for a larger amount of span than Wing
1. In flapping systems lift is predominantly generated over the area of the wing closest to
the root as that is the stiffest section of the wing. Therefore, the larger area of increased
stiffness of the 2nd wing is a possible the reason Wing 2 generated more lift than Wing 1.
Figure 8.19: Wing 2 Position, Force & Phase Correlation @ 5 m/s, 4 Hz, & 7.5° AoA
Further comparing the wing positions of Wing 1 and Wing 2 in Figure 8.12 and
Figure 8.19 respectively, the impact of wing flexibility on the angle of attack can be seen
at 150°, 230° and 330° in the flap. It can be seen that Wing 2 mostly stayed parallel to
the ground on the downstroke while on the upstroke having a higher angle of attack. The
high flexibility of Wing 1 caused it to bend too readily to changes in motion. These
abrupt changes caused Wing 1 to buckle, preventing it from increasing its angle of attack
on the upstroke. This resulted in lower average lift and thrust forces.
99
Figure 8.20 shows the aerodynamic force vectors associated with the 5 m/s, 4 Hz,
7.5° AoA case. These vectors show the direction of the total force generated by the
mechanism during one flap. The wingtip position is plotted versus phase to indicate the
point in the flap. The force vectors were obtained by performing a vector sum of the lift
and thrust forces generated by the mechanism as shown in Figure 8.19. From Figure
8.20, it can be seen that at the very beginning of the downstroke the lift force is negative.
It becomes positive at approximately 30° in the flap, reaches its peak at approximately
140°. The vectors always point towards the right of the graph, indicating the forward
position. Once again this means that thrust is constantly being generated.
Figure 8.20: Aerodynamic Force Vectors vs. Wing Position in Flapping Cycle
100
The fourth case was at 5 m/s, 4 Hz, 15° AoA. At this test condition Wing 1 was
again outperformed by Wing 2. The peak lift produced by Wing 1 was 0.05 lbs, while
the peak lift produced by Wing 2 was almost 0.227 lbs. The thrust performance was
increased as well, with the average thrust of 0.022 lbs being generated by Wing 2. The
mechanism produced positive lift at 65° and the rate of lift generation increased steeply
until a peak was reached at about 160°. At this point the wing was just past the
horizontal point with reference to the ground. From this point lift production decreased
to a minimum at about 300° during which point the wing was already well on its way on
the upstroke.
Figure 8.21: Wing 2 Position, Force & Phase Correlation @ 5 m/s, 4 Hz, & 15° AoA
Comparing Figure 8.13 with Figure 8.21, there are two points where the role of
wing flexibility is evident: 75° and approximately 300°. The increased stiffness of Wing
101
2 caused a sharp increase in lift at 75° as opposed to Wing 1, which increased to its point
of peak lift gradually. The second point was the minimum in lift force at about 300° with
Wing 2. There was an abrupt change from negative lift generation to positive lift
generation, and the cause is most likely the sharp rise in angle of attack with Wing 2.
Looking at the same point in Figure 8.13, it can be seen that the wing has buckled and the
angle of attack on the upstroke is lower than that in Wing 2.
8.5.2
Wing 2 Velocity Analysis
A velocity analysis described similar to that described in Section 8.4.4 was
performed on Wing 2 to examine the role of flexibility on relative velocity. Again
starting with the 0 m/s, 3 Hz, 0° AoA case, it was found that the velocity of the wing’s
root was approximately 0.48 m/s. It was no surprise that the speed of the wing root was
about equal as that of Wing 1 for the same flapping condition. The deviation was due to
slight variances in the flapping frequency around the nominal value. For example the
actual flapping frequency for this case with Wing 1 was 3.2 Hz, but with Wing 2 it was
2.9 Hz. The velocity of a rigid wing at the ¾ span point was extrapolated to be 2.88 m/s,
and 3.84 m/s at the wingtip. The velocity of the flexible wing at the ¾ point was found to
be 3.2 m/s and approximately 4.91 m/s at the wingtip. This was as expected as the
second wing was less flexible than Wing 1, but still more flexible than a purely rigid
wing. Again, this increased performance with respect to a purely rigid wing was due to
the flexible wing’s bending ability as it passed through the maximum velocity point in the
flapping cycle.
The second case was the 5 m/s, 3 Hz, 7.5° AoA case where the root velocity was
0.51 m/s. Extrapolating a rigid wing out to the ¾ span point yielded a wing velocity of
102
3.06 m/s, and 4.08 m/s at the tip. The wing velocity of the flexible wing at the ¾ span
point was 3.47 m/s, and the velocity at the tip was approximately 5.1 m/s. Again, it can
be seen that the velocities of Wing 2 were slightly less than the velocities of Wing 1, but
higher than that of a purely rigid wing. With the inclusion of the incoming flow of 5 m/s
the velocity of the flexible wing at the ¾ point was approximately 6.09 m/s, while the
rigid wing would be 5.86 m/s. This shows that Wing 2 caused a higher relative wind than
a purely rigid wing, and this should in theory produce more lift force.
The third case was again taken to be 5 m/s, 4 Hz, 7.5° AoA. The root velocity at
this point was 0.55 m/s. The velocity of a purely rigid wing at the ¾ point would be 3.42
m/s and would be 4.56 m/s at the wing tip. The ¾ span point of the flexible wing had a
velocity of approximately 4.11 m/s. With the incoming flow of 5 m/s, the velocity of the
air moved by the flexible wing was 6.47 m/s, while the air moved by a rigid wing would
be 6.06 m/s.
The fourth and final case was 5 m/s, 4 Hz, 15° AoA. The velocity of the root was
0.54 m/s. Again, velocities of a rigid wing would be 3.24 m/s and 4.32 m/s for the ¾
span point and the wing tip respectively. The velocity of Wing 2 at this ¾ span point was
found to be approximately 3.92 m/s. The incoming flow of 5 m/s caused air to have a
velocity of 6.35 m/s at the ¾ span point, while its rigid counterpart would cause air to
move at a velocity of 5.95 m/s. Again, this wing moved air at a faster velocity than a
rigid wing, but slower air than the more flexible Wing 1. Although the air velocity is less
than Wing 1, the lift and thrust forces generated are far greater. This suggests that
although it is helpful to have a flexible wing, there is some point where having too much
flexibility has adverse effects.
103
8.6
Summary of Wing 1 and Wing 2 Performance
Figure 8.22 through Figure 8.25 show the increased performance of Wing 2 over
Wing 1. Table 8.1 below shows a summary of wing root and tip velocities of Wing 1 and
Wing 2 in addition to peak and average lift and thrust forces between both sets of wings.
Table 8.1: Summary of Experimental Results
Condition
0 m/s, 3
Hz, 0°
AoA
5 m/s, 3
Hz, 7.5°
AoA
5 m/s, 4
Hz, 7.5°
AoA
5 m/s, 4
Hz, 15°
AoA
Wing
Wing
1:
Wing
2:
Rigid
(Avg):
Wing
1:
Wing
2:
Rigid
(Avg):
Wing
1:
Wing
2:
Rigid
(Avg):
Wing
1:
Wing
2:
Rigid
(Avg):
Root
Velocity
(m/s)
3/4
Span
Point
Velocity
(m/s)
Velocity
of 3/4
Point
with 5
m/s
Flow
(m/s)
Peak
Lift
(lb)
Average
Lift (lb)
Peak
Net
Thrust
(lb)
Average
Thrust
(lb)
0.50
3.50
N/A
0.036
0.009
0.011
0.010
0.48
3.20
N/A
0.080
0.019
0.034
0.032
0.49
2.94
N/A
N/A
N/A
N/A
N/A
0.54
3.71
6.22
0.038
0.004
0.053
0.051
0.51
3.47
6.09
0.199
0.075
0.051
0.050
0.53
3.19
5.38
N/A
N/A
N/A
N/A
0.64
4.50
6.73
0.052
0.043
0.019
0.017
0.55
4.11
6.47
0.293
0.143
0.068
0.067
0.60
3.62
6.18
N/A
N/A
N/A
N/A
0.62
4.30
6.60
0.036
0.001
-0.003
-0.007
0.54
3.92
6.35
0.227
0.040
0.022
0.022
0.58
3.47
6.08
N/A
N/A
N/A
N/A
From Table 8.1 above and the figures below, it can be seen that there was a
dramatic increase in lift and thrust generated by the second, stiffer wing. The shapes of
104
the lift curves of both wings exhibit similar sinusoidal type shapes. The thrust curves
generated by both wings are similar in that both sets appear to generate constant force.
Lift is predominantly generated on the downstroke, with negative lift being
generated on the upstroke, matching conventional knowledge. The increase in positive
lift and thrust was attributed to the stiffer nature of the wing structural members. As
previously mentioned in Section 8.4.4, the flexible wings appeared to show increased
performance over their rigid counterparts. However, it is believed that if a wing is too
flexible it will have adverse effects, as described in Section 8.1.
From the figures below, it can be seen that the lift curves are generally sinusoidal
in nature while the thrust curves are closer to constant functions. In all cases the second
wing produced more peak lift and average lift and thrust than the first wing. Figure 8.23
and Figure 8.24 show that the 7.5° angle of attack produced more average lift than the
other cases with the second set of wings. The duration of positive lift was greatest for
these two cases as well, with both wings exhibiting multiple peaks of positive lift. The
graphs show that both wings produced their peak lift at approximately the same point in
the flapping cycle, within that testing scenario.
105
Figure 8.22: Lift & Thrust vs. Phase @ 0 m/s, 3 Hz, & 0° AoA
Figure 8.23: Lift & Thrust vs. Phase @ 5 m/s, 3 Hz, & 7.5° AoA
106
Figure 8.24: Lift & Thrust vs. Phase @ 5 m/s, 4 Hz, & 7.5° AoA
Figure 8.25: Lift & Thrust vs. Phase @ 5 m/s, 4 Hz, & 15° AoA
107
CHAPTER 9: UNCERTAINTY ANALYSIS
Since this thesis was inpart concerned with experimental testing, it was important
to look at the various sources of uncertainty. There were two primary sources where
uncertainty was a factor in this research. The first was in calibrating the force balance
and the second was in the repeatability associated with the lift and thrust data acquisition
and analysis.
9.1
Force Balance Uncertainty
As previously described in Section 6.2 the force balance used for testing needed to
be calibrated. This involved measuring new spring constants in the force balance. In
order to obtain values as accurate as possible, the experiment to measure the values of the
new spring constants were repeated 3 times and averaged. Table A.1 and Table A.2 show
the data from these experiments. Table 9.1 below displays the average, standard
deviation and variance values for the data obtained from measuring the spring constants.
Table 9.1: Error Analysis for Force Balance
Force
(lb)
0.044
0.066
0.110
0.220
0.331
0.441
Thrust/Drag Direction
Std.
Average
Variance
Dev
4.412
-0.096
0.009
4.380
-0.145
0.021
4.171
-0.086
0.007
3.875
-0.028
0.001
3.334
-0.226
0.051
3.519
-0.001
0.000
Force
(lb)
0.450
1.006
1.550
2.108
2.650
108
Lift Direction
Std.
Average
Variance
Dev
3.970
0.027
0.001
3.086
0.068
0.005
2.216
0.086
0.007
1.220
0.074
0.005
0.322
0.013
0.000
The methods used for the uncertainty analysis are from the book Experimentation
and Uncertainty Analysis for Engineers, by Coleman and Steele [25]. In Table 9.1 the
standard deviation and the variance were obtained from Equation 9.1 and Equation 9.2
respectively.
SX =
1 N
∑ Xi − X
N − 1 i =1
)
S X2 =
1 N
∑ Xi − X
N − 1 i =1
)
(
(
1/ 2
Equation 9.1
Equation 9.2
From the above data in Table 9.1 it can be seen that the error associated with the
measurements from the 3 trials was small and showed repeatability. Thus, allowing the
results to be used in calculating the required spring constants to obtain lift and thrust
force values.
9.2
Lift and Thrust Uncertainty
Figure 9.1 below shows a plot of the uncertainty associated with the lift and forces
at the 5 m/s, 4 Hz, 7.5° AoA with Wing 2. This case was chosen because it had the
conditions which generated the highest aerodynamic forces. The graph below shows the
error (represented by error bars) in the measurement system from flap to flap in one test.
This was done by having the mechanism flap 10 flap cycles at the aforementioned case,
and averaging the lift and thrust data over 10 flaps for each point in the flap. From this
calculation mean thrust and lift forces were obtained. The standard deviation of the mean
109
for each point in the flap was found using Equation 9.1. Estimating a t distribution and
95% confidence interval, error bars were found.
Figure 9.1: Uncertainty Curve for 5 m/s, 4 Hz, 7.5° AoA with Wing 2
From the graph it can be seen that the error for the lift curve is quite small, an
average of approximately ±0.015 lbs at each point. The error in thrust force is even
smaller, an average of approximately 0.01 lbs at each point. This shows that there was
very little variability in lift and thrust forces generated by each individual flap in the 10
flap cycle. The smallest force applied to the force balance was 0.044 lbs in the
calibration stage. The smallest amount of error shown above was approximately 0.01 lbs.
In order to make sure that the force balance was indeed capable of registering at this low
weight, a 0.01 lb load was applied to it and there was indeed a change in displacement.
110
Figure 9.2 below shows day to day repeatability between tests for the 5 m/s, 4 Hz,
7.5° AoA case. Two additional tests were carried out on two separate days and their
cycle averaged lift and thrust values were compared to those of the initial test. Again, the
analysis was performed with this case because the aerodynamic forces generated were the
highest and because of this noise should be lower when compared with other test
conditions where the forces were less.
Figure 9.2: Repeatability 5 m/s, 4 Hz, 7.5° AoA with Wing 2
From Figure 9.2 above, it can be seen that there is very variation in day to day
repeatability. Both the lift and thrust curves from day 2 and day 3 match those the lift
and thrust curves from day 1 quite closely.
111
In order to see how the error scaled with force, the experimental error was found
for the 0 m/s, 3 Hz, 0° AoA case with Wing 1. A plot of this can be seen in Figure 9.3
below. Again, 6 points were selected based on the high speed video analysis as described
in Chapter 8 and plotted with a 95% confidence interval t distribution. From the graph it
can be seen that the error bars are relatively much larger than with the 5 m/s, 4 Hz, 7.5°
AoA case.
Figure 9.3: Uncertainty Curve for 0m/s, 3 Hz, 0° AoA with Wing 1
The average standard deviation for the lift case was approximately 0.01 lbs, and
0.02 lbs for the thrust. It can be seen that the highest error was at 75° and 225°. At these
positions in the flap, the wing was traveling at the lowest velocities, either just starting
the downstroke or the upstroke. The maximum error at this point was 0.014 lbs, while
112
the least error occurred at the minimum and maximum points where the error was 0.01
lbs. At these locations the wing was traveling with the fastest velocity.
The main reason that there was more error associated with this test situation was
most likely due to the very low forces involved. The peak lift generated during this case
was only 0.036 lbs, while the average thrust generated was approximately 0.1 lbs. It is
possible that noise in the system could be a factor in contributing to the error as the
system worked at the lower end of its operating envelope. The error here is acceptable
because it is very unlikely that the mechanism will be operating at these conditions again
due to the very low forces generated.
113
CHAPTER 10: CONCLUDING REMARKS
10.1 Summary
This thesis attempted to investigate the role of wing flexibility in flapping wing
flight. Considerable effort was put into designing and fabricating a low budget
mechanism capable of producing controllable flapping motions and passive flapping
motions. The mechanism was made from lightweight materials and used inexpensive
commercial off the shelf parts. In designing the mechanism, it was found that the best
way to produce flapping motions was through the use of a scotch yoke/crankshaft
mechanism. Both motions were produced through a single motor. It was also found that
the motor used to provide the flapping motions, while able to accomplish the task of
flapping at the target frequencies, was slightly underpowered. It would be better to use a
stronger motor, although the increased weight would be a factor to consider.
Additionally, it was found that the mechanism was still too heavy. Although after
the weight reduction efforts the mechanism’s weight was significantly reduced,
additional work could be done to streamline the body removing excess material. Two
elements of the design which contributed most to the weight were the aluminum bearing
and motor mounts as well as the linear ball bearing which allowed the mechanism to
translate in the vertical axis. Aluminum was chosen because of its ready availability and
low cost. Using more expensive but lighter materials in its place, it would be possible to
reduce the weight significantly. It was found that the linear ball bearings were over
specified for the 0.5 inch vertical shaft over which they rode. Using a smaller vertical
shaft would allow for the use of smaller and lighter bearings.
114
Two families of flexible wings were fabricated, tested and built using carbon fiber
and fiberglass. These wings were simplified versions of wings from a large bat. There
were some important lessons learned from fabricating and testing the flexible wings. It
was better to have a stiff leading edge, so the wing did not buckle and lose stability. The
major lesson learned from the fabrication process was that it was very helpful to have a
mold system which allowed for the repeated fabrication of symmetric wings.
To test the flapping wing mechanism, a force balance testing structure was
designed and built as well. In designing the force balance, it was found that friction
played a large role. The first design, which used linear ball bearings to allow the
mechanism to traverse, had too great of a static friction coefficient. Switching to an air
bearing eliminated this problem.
The force balance was carefully calibrated and instrumented with position sensors
to measure lift and thrust forces. In order to simulate the mechanism flying in an air
stream at low speeds, an existing wind tunnel was converted into into an open flow tunnel
capable of achieving air speeds as low as 5 meters per second. An evolving test matrix
was created and used in a comprehensive testing process. Data acquired from the
mechanism encoder, force balance position transducers and high video were analyzed.
When measuring the aerodynamic forces produced in the experiments, it was
found that thrust was constantly generated, while lift was periodic in nature following a
sinusoidal trend. It was found that lift is predominantly generated on the downstroke,
with negative lift being generated on the upstroke. Using a high speed video camera, the
shape of the flexible wing was found as well as the velocities of the wing at various
points in the cycle. The wing positions of highest velocity generally had the highest
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magnitudes of lift. It was also shown that the relative wind over the wing increased due
to the flexible nature of the wing, thus potentially enhancing lift.
It was found that a more flexible wing generated higher velocities. Wing 1
generally traveled at a higher velocity when flapping than did Wing 2. Since lift is
proportional to the square of velocity, the lift should theoretically be greater. However,
the forces generated by Wing 1 were very small when compared to Wing 2. This led to
the conclusion that although there are benefits to having a flexible wing, there is some
limit where an overly flexible wing generates less lift than its slightly more rigid (but still
flexible) counterpart. The main reason believed to cause this was the lack of structural
support during changes in stroke. It was shown that the flexible wing buckled a
phenomenon which although may have some positive effects, appear to be a hindrance
when extreme.
Also from the data, it can be seen that the best test case situation was the 5 m/s, 4
Hz, 7.5° AoA case. It has already been shown that 4 Hz is a frequency at which some
natural flyers flap. The increased flow stream had positive effects as well, helping
provide additional lift, as did the positive angle of attack. Results showed that increasing
the angle of attack was helpful only to a point. When the angle of attack was too high
flow separation occurred. This caused turbulent boundary layers to form and adversely
effect lift and thrust generation.
It was found that phase lag also played an important role in flapping wing flight.
Wing 1 experienced greater phase lag than did the stiffer Wing 2. For Wing 1 it was
found that the phase lag at the center of the upstroke was approximately 58° while the
phase lag at the end of the downstroke was an average of 35.5°. Through the images
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acquired from the high speed video camera, it was found that when the wing’s root was at
the center of the upstroke, the lagging tip caused the wing’s leading spar to buckle. This
loss of structural stability was most likely the cause of Wing 1’s poor performance in
generating aerodynamic loads.
Stiffening the wing proved to have beneficial effects in reducing phase lag. Wing 2
had an average of 23.5° phase lag at the center of the upstroke and 27.6° at the end of the
downstroke. A parallel can be drawn between this flexing nature of the leading edge of
the wing and the ability of a flexible wing being able to correct for such natural
phenomena such as gusts or collision with a stationary object. The wings were capable of
changing their physical structure along the leading edge and still produce lift and thrust;
this is a major advantage of flexible wings over rigid ones.
10.2 Contributions to Research Area
This research was done primarily as a learning effort to better understand the role
of wing flexibility in flapping wing flight. The work done has contributed to the area of
flapping wing UAV research for vehicles with membrane wings. The studying of two
wings, various flapping frequencies and air flows will help future researchers in perhaps
eventually building a flapping wing UAV with flexible membrane wings. The research
done in this thesis was done on a very low budget, approximately 500 dollars plus the
cost of machining time.
The prototype which was built produced 0.3 lbs of lift in its best case and 0.05 lbs
of net thrust, overcoming its own drag. The mechanism was a wind tunnel model which
weighed approximately 1.8 lbs. With a higher budget it may be able to decrease the
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weight further. For example, if the weight was cut in half, and the lift was increased by a
factor of 5 based on continued research (new wings and testing scenarios) it would be
possible to build a mechanism capable of supporting its own weight and possibly flying.
Perhaps most importantly this research has planted the seeds to allow Georgia Tech
to gain a better understanding of flapping wing flight. The modified open air wind tunnel
facility, existing mechanism as well as force balance test bed lay the ground work for
future experiments in this area giving the Georgia Tech Research Institute a 1 to 2 year
head start.
10.3 Future Work
There is still considerable research must be done to fully understand the problem at
hand. Starting at a smaller level there is so much more which can be done to improve on
and better understand the device built in this research effort.
One of the most noticeable things was the motor was under powered. There was a
trade off between cost, motor torque and weight. An obvious answer would be to use a
motor with more torque. It would also be possible to implement a feedback control
system to help keep the speed of the flap constant. Perhaps it is better to implement a
feedback control algorithm which varies the speed of the wings in mid-flap. These are
things which would be better determined through additional testing.
Another interesting feature would be to introduce variable pitch control in the
device. The device built in this research was capable of producing passive pitching
motions which were functions of wing phase during the flap. Additionally, the
aerodynamics of flapping wing flight is not well understood and an extremely difficult
118
problem to tackle. Additional work needs to be done on theoretical modeling using CFD
codes, and trying to match these results with PIV flow visualization techniques to observe
airflow patterns as the wing flaps. FEA analysis as well as using laser vibrometers on the
wings would lead to better understanding wing deformation and loads seen at various
points along the structural members.
Finally additional wings should be fabricated and tested. The wings used in this
research all consisted of the same materials: carbon fiber structures with fiberglass
membranes. Additional wings of various different materials or perhaps even wings
which follow different structure patterns should be built and tested.
These are just some recommendations which will help understand the dynamics
behind flapping wing flight, with the goal of eventually building an ornithopter with
flexible wings capable of sustained flight.
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APPENDIX A: CALIBRATION DATA
Table A.1 below shows the spring calibration data used to estimate spring
constants of the springs used to measure lift and thrust. The experiments were repeated
three times to get accurate measurements and minimize error
Table A.1: Spring Constant Calibration Data
Force
g
20
30
50
100
150
200
lb
0.044
0.066
0.110
0.220
0.331
0.441
Force
g
20
30
50
100
150
200
lb
0.044
0.066
0.110
0.220
0.331
0.441
Force
g
20
30
50
100
150
200
lb
0.044
0.066
0.110
0.220
0.331
0.441
Test 1
Displacement
Thrust/Drag (in)
4.302
4.214
4.145
3.890
3.073
3.519
Force
lb
0.450
1.006
1.550
2.108
2.650
Displacement
Lift (in)
3.976
3.012
2.261
1.147
0.329
Test 2
Displacement
Thrust/Drag (in)
4.451
4.447
4.101
3.843
3.473
3.520
Force
lb
0.450
1.006
1.550
2.108
2.650
Displacement
Lift (in)
3.941
3.101
2.116
1.218
0.307
Test 3
Displacement
Thrust/Drag (in)
4.482
4.479
4.267
3.893
3.455
3.519
Force
lb
0.450
1.006
1.550
2.108
2.650
Displacement
Lift (in)
3.994
3.146
2.270
1.294
0.329
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The data from Table A.1, the values were averaged and entered into Table A.2.
Table A2: Averaged Values of Spring Calibration Data
lb
0.044
0.066
0.110
0.220
0.331
0.441
Avg. Thrust/Drag
4.412
4.380
4.171
3.875
3.334
3.519
Experimental k:
Theoretical k:
Used k:
-0.32 lb/in
0.29 lb/in
0.32 lb/in
lb
0.450
1.006
1.550
2.108
2.650
Avg. Top
3.970
3.086
2.216
1.220
0.322
-0.60 lb/in
0.56 lb/in
0.60 lb/in
From Table A.2, the spring constants under the row “Used k” represent those
which were actually used in the LabView VI to obtain a force measurement.
Figure A.1: Spring Constant Data for Force Balance Calibration
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APPENDIX B: PLOTS
Figure B.1: Wing 1 Root, Tip & Encoder Position vs. Time @ 0 m/s, 2 Hz, 7.5° AoA
Figure B.2: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 2 Hz, 7.5° AoA
122
Figure B.3: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 3 Hz, 0° AoA
Figure B.4: Wing 1 Root, Tip & Encoder Position vs. Time @ 0 m/s, 3 Hz, 7.5° AoA
123
Figure B.5: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 3 Hz, 7.5° AoA
Figure B.6: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 4 Hz, 0° AoA
124
Figure B.7: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 4 Hz, 7.5° AoA
Figure B.8: Wing 1 Root, Tip & Encoder Position vs. Time @ 5 m/s, 4 Hz, 15° AoA
125
Figure B. 9: Lift & Thrust vs. Phase @ 0 & 5 m/s, 2 Hz, & 7.5° AoA
Figure B.10: Lift & Thrust vs. Phase @ 0 m/s, 3 Hz, & 0° & 7.5° AoA
126
Figure B.11: Lift & Thrust vs. Phase @ 5 m/s, 3 Hz, & 0° & 7.5° AoA
Figure B.12: Lift & Thrust vs. Phase @ 5 m/s, 4 Hz, & 0°, 7.5° & 15° AoA
127
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